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breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Mihalache%2C+D&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Mihalache%2C+D&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Mihalache%2C+D&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.10667">arXiv:2411.10667</a> <span> [<a href="https://arxiv.org/pdf/2411.10667">pdf</a>, <a href="https://arxiv.org/ps/2411.10667">ps</a>, <a href="https://arxiv.org/format/2411.10667">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> Solitons in composite linear-nonlinear moir茅 lattices </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Zeng%2C+L">Liangwei Zeng</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Li%2C+J">Jingzhen Li</a>, <a href="/search/?searchtype=author&query=Zhu%2C+X">Xing Zhu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.10667v1-abstract-short" style="display: inline;"> We produce families of two-dimensional gap solitons (GSs) maintained by moir茅 lattices (MLs) composed of linear and nonlinear sublattices, with the defocusing sign of the nonlinearity. Depending on the angle between the sublattices, the ML may be quasiperiodic or periodic, composed of mutually incommensurate or commensurate sublattices, respectively (in the latter case, the inter-lattice angle cor… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.10667v1-abstract-full').style.display = 'inline'; document.getElementById('2411.10667v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.10667v1-abstract-full" style="display: none;"> We produce families of two-dimensional gap solitons (GSs) maintained by moir茅 lattices (MLs) composed of linear and nonlinear sublattices, with the defocusing sign of the nonlinearity. Depending on the angle between the sublattices, the ML may be quasiperiodic or periodic, composed of mutually incommensurate or commensurate sublattices, respectively (in the latter case, the inter-lattice angle corresponds to Pythagorean triples). The GSs include fundamental, quadrupole, and octupole solitons, as well as quadrupoles and octupoles carrying unitary vorticity. Stability segments of the GS families are identified by means of the linearized equation for small perturbations, and confirmed by direct simulations of perturbed evolution. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.10667v1-abstract-full').style.display = 'none'; document.getElementById('2411.10667v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 figures, to be published in Optics Letters (2024)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Optics Letters, (2024) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2409.15062">arXiv:2409.15062</a> <span> [<a href="https://arxiv.org/pdf/2409.15062">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> Symmetry-breaking bifurcations of pure-quartic solitons in dual-core couplers </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Li%2C+P">Pengfei Li</a>, <a href="/search/?searchtype=author&query=Dong%2C+L">Liangliang Dong</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2409.15062v1-abstract-short" style="display: inline;"> We investigate spontaneous symmetry- and antisymmetry-breaking bifurcations of solitons in a nonlinear dual-core waveguide with the pure-quartic dispersion and Kerr nonlinearity. Symmetric, antisymmetric, and asymmetric pure-quartic solitons (PQSs) are found, and their stability domains are identified. The bifurcations for both the symmetric and antisymmetric PQSs are of the supercritical type (al… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.15062v1-abstract-full').style.display = 'inline'; document.getElementById('2409.15062v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.15062v1-abstract-full" style="display: none;"> We investigate spontaneous symmetry- and antisymmetry-breaking bifurcations of solitons in a nonlinear dual-core waveguide with the pure-quartic dispersion and Kerr nonlinearity. Symmetric, antisymmetric, and asymmetric pure-quartic solitons (PQSs) are found, and their stability domains are identified. The bifurcations for both the symmetric and antisymmetric PQSs are of the supercritical type (alias phase transitions of the second kind). Direct simulations of the perturbed evolution of PQSs corroborate their stability boundaries predicted by the analysis of small perturbations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.15062v1-abstract-full').style.display = 'none'; document.getElementById('2409.15062v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages, 5 figures, to be published in Optics Letters</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.06555">arXiv:2306.06555</a> <span> [<a href="https://arxiv.org/pdf/2306.06555">pdf</a>, <a href="https://arxiv.org/ps/2306.06555">ps</a>, <a href="https://arxiv.org/format/2306.06555">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.chaos.2023.113701">10.1016/j.chaos.2023.113701 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Second-harmonic generation in the system with fractional diffraction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Li%2C+P">Pengfei Li</a>, <a href="/search/?searchtype=author&query=Sakaguchi%2C+H">Hidetsugu Sakaguchi</a>, <a href="/search/?searchtype=author&query=Zeng%2C+L">Liangwei Zeng</a>, <a href="/search/?searchtype=author&query=Zhu%2C+X">Xing Zhu</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.06555v2-abstract-short" style="display: inline;"> We construct a family of bright optical solitons composed of fundamental frequency (FF) and second-harmonic (SH) components in the one-dimensional (planar) waveguide with the quadratic (second-harmonic-generating) nonlinearity and effective fractional diffraction, characterized by the Levy index 伪, taking values between 2 and 0.5, which correspond to the non-fractional diffraction and critical col… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.06555v2-abstract-full').style.display = 'inline'; document.getElementById('2306.06555v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.06555v2-abstract-full" style="display: none;"> We construct a family of bright optical solitons composed of fundamental frequency (FF) and second-harmonic (SH) components in the one-dimensional (planar) waveguide with the quadratic (second-harmonic-generating) nonlinearity and effective fractional diffraction, characterized by the Levy index 伪, taking values between 2 and 0.5, which correspond to the non-fractional diffraction and critical collapse, respectively. The existence domain and stability boundary for the solitons are delineated in the space of 伪, FF-SH mismatch parameter, and propagation constant. The stability boundary is tantamount to that predicted by the Vakhitov-Kolokolov criterion, while unstable solitons spontaneously evolve into localized breathers. A sufficiently weak transverse kick applied to the stable solitons excite small internal vibrations in the stable solitons, without setting them in motion. A stronger kick makes the solitons' trajectories tilted, simultaneously destabilizing the solitons. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.06555v2-abstract-full').style.display = 'none'; document.getElementById('2306.06555v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">27 pages, 8 figures, to be published in Chaos, Solitons & Fractals</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2302.04146">arXiv:2302.04146</a> <span> [<a href="https://arxiv.org/pdf/2302.04146">pdf</a>, <a href="https://arxiv.org/format/2302.04146">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.chaos.2023.113247">10.1016/j.chaos.2023.113247 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Controlled non-autonomous matter-wave solitons in spinor Bose-Einstein condensates with spatiotemporal modulation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Ding%2C+C">Cui-Cui Ding</a>, <a href="/search/?searchtype=author&query=Zhou%2C+Q">Qin Zhou</a>, <a href="/search/?searchtype=author&query=Xu%2C+S">Si-Liu Xu</a>, <a href="/search/?searchtype=author&query=Sun%2C+Y">Yun-Zhou Sun</a>, <a href="/search/?searchtype=author&query=Liu%2C+W">Wen-Jun Liu</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2302.04146v1-abstract-short" style="display: inline;"> To study controlled evolution of non-autonomous matter-wave solitons in spinor Bose-Einstein condensates with spatiotemporal modulation, we focus on a system of three coupled Gross-Pitaevskii (GP) equations with space-time-dependent external potentials and temporally modulated gain/loss distributions. An integrability condition and a non-isospectral Lax pair for the coupled GP equations are obtain… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.04146v1-abstract-full').style.display = 'inline'; document.getElementById('2302.04146v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2302.04146v1-abstract-full" style="display: none;"> To study controlled evolution of non-autonomous matter-wave solitons in spinor Bose-Einstein condensates with spatiotemporal modulation, we focus on a system of three coupled Gross-Pitaevskii (GP) equations with space-time-dependent external potentials and temporally modulated gain/loss distributions. An integrability condition and a non-isospectral Lax pair for the coupled GP equations are obtained. Using it, we derive an infinite set of dynamical invariants, the first two of which are the mass and momentum. The Darboux transform is used to generate one- and two-soliton solutions. Under the action of different external potentials and gain/loss distributions, various solutions for controlled non-autonomous matter-wave solitons of both ferromagnetic and polar types are obtained, such as self-compressed, snake-like and stepwise solitons, and as well as breathers. In particular, the formation of states resembling rogue waves, under the action of a sign-reversible gain-loss distribution, is demonstrated too. Shape-preserving and changing interactions between two non-autonomous matter-wave solitons and bound states of solitons are addressed too. In this context, spin switching arises in the polar-ferromagnetic interaction. Stability of the non-autonomous matter-wave solitons is verified by means of systematic simulations of their perturbed evolution. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2302.04146v1-abstract-full').style.display = 'none'; document.getElementById('2302.04146v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 February, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">to be published in Chaos, Solitons & Fractals</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2212.07610">arXiv:2212.07610</a> <span> [<a href="https://arxiv.org/pdf/2212.07610">pdf</a>, <a href="https://arxiv.org/ps/2212.07610">ps</a>, <a href="https://arxiv.org/format/2212.07610">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> Stabilization of Axisymmetric Airy Beams by Means of Diffraction and Nonlinearity Management in Two-Dimensional Fractional Nonlinear Schr枚dinger Equations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Li%2C+P">Pengfei Li</a>, <a href="/search/?searchtype=author&query=Wei%2C+Y">Yanzhu Wei</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2212.07610v1-abstract-short" style="display: inline;"> The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schr枚dinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and L茅vy index ((LI) alias for the fractionality) taking values $1\leq伪\leq 2$. The model applies to light propagation in a chain of optical cavities emulating fractional diffraction. Manageme… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.07610v1-abstract-full').style.display = 'inline'; document.getElementById('2212.07610v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2212.07610v1-abstract-full" style="display: none;"> The propagation dynamics of two-dimensional (2D) ring-Airy beams is studied in the framework of the fractional Schr枚dinger equation, which includes saturable or cubic self-focusing or defocusing nonlinearity and L茅vy index ((LI) alias for the fractionality) taking values $1\leq伪\leq 2$. The model applies to light propagation in a chain of optical cavities emulating fractional diffraction. Management is included by making the diffraction and/or nonlinearity coefficients periodic functions of the propagation distance, $味$. The management format with the nonlinearity coefficient decaying as $1/味$ is considered, too. These management schemes maintain stable propagation of the ring-Airy beams, which maintain their axial symmetry, in contrast to the symmetry-breaking splitting instability of ring-shaped patterns in 2D Kerr media. The instability driven by supercritical collapse at all values $伪< 2$ in the presence of the self-focusing cubic term is eliminated, too, by the means of management. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2212.07610v1-abstract-full').style.display = 'none'; document.getElementById('2212.07610v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 December, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 7 figures,to be published in Symmetry, special issue on " Symmetry in Nonlinear Optics: Topics and Advances"</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.07356">arXiv:2207.07356</a> <span> [<a href="https://arxiv.org/pdf/2207.07356">pdf</a>, <a href="https://arxiv.org/format/2207.07356">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> </div> <p class="title is-5 mathjax"> General higher-order breathers and rogue waves in the two-component long-wave--short-wave resonance-interaction model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Rao%2C+J">Jiguang Rao</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=He%2C+J">Jingsong He</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.07356v1-abstract-short" style="display: inline;"> General higher-order breather and rogue wave (RW) solutions to the two-component long wave--short wave resonance interaction (2-LSRI) model are derived via the bilinear Kadomtsev-Petviashvili hierarchy reduction method and are given in terms of determinants. Under particular parametric conditions, the breather solutions can reduce to homoclinic orbits, or a mixture of breathers and homoclinic orbi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.07356v1-abstract-full').style.display = 'inline'; document.getElementById('2207.07356v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.07356v1-abstract-full" style="display: none;"> General higher-order breather and rogue wave (RW) solutions to the two-component long wave--short wave resonance interaction (2-LSRI) model are derived via the bilinear Kadomtsev-Petviashvili hierarchy reduction method and are given in terms of determinants. Under particular parametric conditions, the breather solutions can reduce to homoclinic orbits, or a mixture of breathers and homoclinic orbits. There are three families of RW solutions, which correspond to a simple root, two simple roots, and a double root of an algebraic equation related to the dimension reduction procedure. The first family of RW solutions consists of $\frac{N(N+1)}{2}$ bounded fundamental RWs, the second family is composed of $\frac{N_1(N_1+1)}{2}$ bounded fundamental RWs coexisting with another $\frac{N_2(N_2+1)}{2}$ fundamental RWs of different bounded state ($N,N_1,N_2$ being positive integers), while the third one have ${[\widehat{N}_1^2+\widehat{N}_2^2-\widehat{N}_1(\widehat{N}_2-1)]}$ fundamental bounded RWs ($\widehat{N}_1,\widehat{N}_2$ being non-negative integers). The second family can be regarded as the superpositions of the first family, while the third family can be the degenerate case of the first family under particular parameter choices. These diverse RW patterns are illustrated graphically. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.07356v1-abstract-full').style.display = 'none'; document.getElementById('2207.07356v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">This paper contains 32 panges,10 figures and will be published in journal " Stud. Appl. Math."</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.00443">arXiv:2111.00443</a> <span> [<a href="https://arxiv.org/pdf/2111.00443">pdf</a>, <a href="https://arxiv.org/ps/2111.00443">ps</a>, <a href="https://arxiv.org/format/2111.00443">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.chaos.2021.111586">10.1016/j.chaos.2021.111586 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quadratic fractional solitons </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Zeng%2C+L">Liangwei Zeng</a>, <a href="/search/?searchtype=author&query=Zhu%2C+Y">Yongle Zhu</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Wang%2C+Q">Qing Wang</a>, <a href="/search/?searchtype=author&query=Long%2C+H">Hu Long</a>, <a href="/search/?searchtype=author&query=Cai%2C+Y">Yi Cai</a>, <a href="/search/?searchtype=author&query=Lu%2C+X">Xiaowei Lu</a>, <a href="/search/?searchtype=author&query=Li%2C+J">Jingzhen Li</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.00443v2-abstract-short" style="display: inline;"> We introduce a system combining the quadratic self-attractive or composite quadratic-cubic nonlinearity, acting in the combination with the fractional diffraction, which is characterized by its L茅vy index $伪$. The model applies to a gas of quantum particles moving by L茅vy flights, with the quadratic term representing the Lee-Huang-Yang correction to the mean-field interactions. A family of fundame… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.00443v2-abstract-full').style.display = 'inline'; document.getElementById('2111.00443v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.00443v2-abstract-full" style="display: none;"> We introduce a system combining the quadratic self-attractive or composite quadratic-cubic nonlinearity, acting in the combination with the fractional diffraction, which is characterized by its L茅vy index $伪$. The model applies to a gas of quantum particles moving by L茅vy flights, with the quadratic term representing the Lee-Huang-Yang correction to the mean-field interactions. A family of fundamental solitons is constructed in a numerical form, while the dependence of its norm on the chemical potential characteristic is obtained in an exact analytical form. The family of \textit{quasi-Townes solitons}, appearing in the limit case of $伪=1/2$, is investigated by means of a variational approximation. A nonlinear lattice, represented by spatially periodical modulation of the quadratic term, is briefly addressed too. The consideration of the interplay of competing quadratic (attractive) and cubic (repulsive) terms with a lattice potential reveals families of single-, double-, and triple-peak gap solitons (GSs) in two finite bandgaps. The competing nonlinearity gives rise to alternating regions of stability and instability of the GS, the stability intervals shrinking with the increase of the number of peaks in the GS. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.00443v2-abstract-full').style.display = 'none'; document.getElementById('2111.00443v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">to be published in Chaos, Solitons and Fractals</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2110.00185">arXiv:2110.00185</a> <span> [<a href="https://arxiv.org/pdf/2110.00185">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> </div> <p class="title is-5 mathjax"> Airy-Gaussian vortex beams in the fractional nonlinear-Schr枚dinger medium </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=He%2C+S">Shangling He</a>, <a href="/search/?searchtype=author&query=Zhou%2C+K">Kangzhu Zhou</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Zhang%2C+L">Liping Zhang</a>, <a href="/search/?searchtype=author&query=Tu%2C+J">Jialong Tu</a>, <a href="/search/?searchtype=author&query=Wu%2C+Y">You Wu</a>, <a href="/search/?searchtype=author&query=Zhao%2C+J">Jiajia Zhao</a>, <a href="/search/?searchtype=author&query=Peng%2C+X">Xi Peng</a>, <a href="/search/?searchtype=author&query=He%2C+Y">Yingji He</a>, <a href="/search/?searchtype=author&query=Zhou%2C+X">Xiang Zhou</a>, <a href="/search/?searchtype=author&query=Deng%2C+D">Dongmei Deng</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2110.00185v1-abstract-short" style="display: inline;"> We address the propagation of vortex beams with the circular Airy-Gaussian shape in a (2+1)-dimensional optical waveguide modeled by the fractional nonlinear Schrodinger equation. Systematic analysis of autofocusing of the beams reveals a strongly non-monotonous dependence of the peak intensity in the focal plane on the corresponding Levy index, with a strong maximum at alpha =1.4. Effects of the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.00185v1-abstract-full').style.display = 'inline'; document.getElementById('2110.00185v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2110.00185v1-abstract-full" style="display: none;"> We address the propagation of vortex beams with the circular Airy-Gaussian shape in a (2+1)-dimensional optical waveguide modeled by the fractional nonlinear Schrodinger equation. Systematic analysis of autofocusing of the beams reveals a strongly non-monotonous dependence of the peak intensity in the focal plane on the corresponding Levy index, with a strong maximum at alpha =1.4. Effects of the nonlinearity strength, the ratio of widths of the Airy and Gaussian factors in the input, as well as the beam vorticity, on the autofocusing dynamics are explored. In particular, multiple autofocusing events occur if the nonlinearity is strong enough. Under the action of the azimuthal modulational instability, an axisymmetric beam may split into a set of separating bright spots. In the case of strong fractality (for alpha close to 1), the nonlinear beam self-traps, after the first instance of autofocusing, into a breathing vortical quasi-soliton. Radiation forces induced by the beam field are considered too, and a capture position for a probe nanoparticle is thus identified. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.00185v1-abstract-full').style.display = 'none'; document.getElementById('2110.00185v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 September, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17pages,11figures,to be published in J. Opt. Soc. Am. B</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> In 2021 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2108.06146">arXiv:2108.06146</a> <span> [<a href="https://arxiv.org/pdf/2108.06146">pdf</a>, <a href="https://arxiv.org/ps/2108.06146">ps</a>, <a href="https://arxiv.org/format/2108.06146">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s11071-021-06834-0">10.1007/s11071-021-06834-0 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Flat-floor bubbles, dark solitons, and vortices stabilized by inhomogeneous nonlinear media </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Zeng%2C+L">Liangwei Zeng</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Cai%2C+Y">Yi Cai</a>, <a href="/search/?searchtype=author&query=Lu%2C+X">Xiaowei Lu</a>, <a href="/search/?searchtype=author&query=Zhu%2C+Q">Qifan Zhu</a>, <a href="/search/?searchtype=author&query=Li%2C+J">Jingzhen Li</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2108.06146v1-abstract-short" style="display: inline;"> We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of flat-floor \textquotedblleft bubbles", and topological excitations, in the form of dark solitons in 1D and vortices with winding number $m$ in 2D. Un… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.06146v1-abstract-full').style.display = 'inline'; document.getElementById('2108.06146v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2108.06146v1-abstract-full" style="display: none;"> We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of flat-floor \textquotedblleft bubbles", and topological excitations, in the form of dark solitons in 1D and vortices with winding number $m$ in 2D. Unlike bright solitons, delocalized bubbles and dark modes were not previously considered in this setting. The ground and excited states are accurately approximated by the Thomas-Fermi expressions. The 1D and 2D bubbles, as well as vortices with $m=1$, are completely stable, while the dark solitons and vortices with $m=2$ have nontrivial stability boundaries in their existence areas. Unstable dark solitons are expelled to the periphery, while unstable double vortices split in rotating pairs of unitary ones. Displaced stable vortices precess around the central point. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.06146v1-abstract-full').style.display = 'none'; document.getElementById('2108.06146v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">to be published in Nonlinear Dynamics</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nonlinear Dyn. 106(1), 815-830 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2106.05446">arXiv:2106.05446</a> <span> [<a href="https://arxiv.org/pdf/2106.05446">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> </div> <p class="title is-5 mathjax"> Symmetry-breaking bifurcations and ghost states in the fractional nonlinear Schr枚dinger equation with a PT-symmetric potential </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Li%2C+P">Pengfei Li</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2106.05446v1-abstract-short" style="display: inline;"> We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schr枚dinger equation with the cubic or cubic-quintic (CQ) nonlinearity and a parity-time (PT)-symmetric potential, which may be realized in optical cavities. Solitons are destabilized at the bifurcation point, and, in the case of the CQ nonlinearity, the stability is restored by an inverse bifurcation. Two mutually-… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.05446v1-abstract-full').style.display = 'inline'; document.getElementById('2106.05446v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2106.05446v1-abstract-full" style="display: none;"> We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schr枚dinger equation with the cubic or cubic-quintic (CQ) nonlinearity and a parity-time (PT)-symmetric potential, which may be realized in optical cavities. Solitons are destabilized at the bifurcation point, and, in the case of the CQ nonlinearity, the stability is restored by an inverse bifurcation. Two mutually-conjugate branches of ghost states (GSs), with complex propagation constants, are created by the bifurcation, solely in the case of the fractional diffraction. While GSs are not true solutions, direct simulations confirm that their shapes and results of their stability analysis provide a blueprint for the evolution of genuine localized modes in the system. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2106.05446v1-abstract-full').style.display = 'none'; document.getElementById('2106.05446v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 June, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 4 figures, to be published in Optics Letters</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2105.00380">arXiv:2105.00380</a> <span> [<a href="https://arxiv.org/pdf/2105.00380">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> </div> <p class="title is-5 mathjax"> Propagation dynamics of radially polarized symmetric Airy beams in the fractional Schr枚dinger equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=He%2C+S">Shangling He</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Peng%2C+X">Xi Peng</a>, <a href="/search/?searchtype=author&query=He%2C+Y">Yingji He</a>, <a href="/search/?searchtype=author&query=Deng%2C+D">Dongmei Deng</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2105.00380v1-abstract-short" style="display: inline;"> We analyze the propagation dynamics of radially polarized symmetric Airy beams (R-SABs) in a (2+1)-dimensional optical system with fractional diffraction, modeled by the fractional Schr枚dinger equation (FSE) characterized by the L茅vy index. The autofocusing effect featured by such beams becomes stronger, while the focal length becomes shorter, with the increase of . The effect of the intrinsic vor… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2105.00380v1-abstract-full').style.display = 'inline'; document.getElementById('2105.00380v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2105.00380v1-abstract-full" style="display: none;"> We analyze the propagation dynamics of radially polarized symmetric Airy beams (R-SABs) in a (2+1)-dimensional optical system with fractional diffraction, modeled by the fractional Schr枚dinger equation (FSE) characterized by the L茅vy index. The autofocusing effect featured by such beams becomes stronger, while the focal length becomes shorter, with the increase of . The effect of the intrinsic vorticity on the autofocusing dynamics of the beams is considered too. Then, the ability of R-SABs to capture nano-particles by means of radiation forces is explored, and multiple capture positions emerging in the course of the propagation are identified. Finally, we find that the propagation of the vortical R-SABs with an off-axis shift leads to rupture of the ring-shaped pattern of the power-density distribution. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2105.00380v1-abstract-full').style.display = 'none'; document.getElementById('2105.00380v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 May, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15pages, 7 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Lett. A 2021 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2104.07209">arXiv:2104.07209</a> <span> [<a href="https://arxiv.org/pdf/2104.07209">pdf</a>, <a href="https://arxiv.org/ps/2104.07209">ps</a>, <a href="https://arxiv.org/format/2104.07209">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.chaos.2020.110589">10.1016/j.chaos.2020.110589 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Families of fundamental and multipole solitons in a cubic-quintic nonlinear lattice in fractional dimension </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Zeng%2C+L">Liangwei Zeng</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Lu%2C+X">Xiaowei Lu</a>, <a href="/search/?searchtype=author&query=Cai%2C+Y">Yi Cai</a>, <a href="/search/?searchtype=author&query=Zhu%2C+Q">Qifan Zhu</a>, <a href="/search/?searchtype=author&query=Li%2C+J">Jingzhen Li</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2104.07209v1-abstract-short" style="display: inline;"> We construct families of fundamental, dipole, and tripole solitons in the fractional Schr枚dinger equation (FSE)\ incorporating self-focusing cubic and defocusing quintic terms modulated by factors $\cos ^{2}x$ and $\sin^{2}x$, respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonli… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.07209v1-abstract-full').style.display = 'inline'; document.getElementById('2104.07209v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2104.07209v1-abstract-full" style="display: none;"> We construct families of fundamental, dipole, and tripole solitons in the fractional Schr枚dinger equation (FSE)\ incorporating self-focusing cubic and defocusing quintic terms modulated by factors $\cos ^{2}x$ and $\sin^{2}x$, respectively. While the fundamental solitons are similar to those in the model with the uniform nonlinearity, the multipole complexes exist only in the presence of the nonlinear lattice. The shapes and stability of all the solitons strongly depend on the L茅vy index (LI)\ that determines the FSE fractionality. Stability areas are identified in the plane of LI and propagation constant by means of numerical methods, and some results are explained with the help of an analytical approximation. The stability areas are broadest for the fundamental solitons and narrowest for the tripoles. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.07209v1-abstract-full').style.display = 'none'; document.getElementById('2104.07209v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 April, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Publised in Chaos, Solitons and Fractals, 144, 110589 (2021)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Chaos Solitons Fract. 144, 110589 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2104.04287">arXiv:2104.04287</a> <span> [<a href="https://arxiv.org/pdf/2104.04287">pdf</a>, <a href="https://arxiv.org/ps/2104.04287">ps</a>, <a href="https://arxiv.org/format/2104.04287">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s11071-021-06459-3">10.1007/s11071-021-06459-3 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Bubbles and W-shaped solitons in Kerr media with fractional diffraction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Zeng%2C+L">Liangwei Zeng</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Cai%2C+Y">Yi Cai</a>, <a href="/search/?searchtype=author&query=Lu%2C+X">Xiaowei Lu</a>, <a href="/search/?searchtype=author&query=Zhu%2C+Q">Qifan Zhu</a>, <a href="/search/?searchtype=author&query=Li%2C+J">Jingzhen Li</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2104.04287v2-abstract-short" style="display: inline;"> We demonstrate that, with the help of a Gaussian potential barrier, dark modes in the form of a local depression ("bubbles") can be supported by the repulsive Kerr nonlinearity in combination with fractional dimension. Similarly, W-shaped modes are supported by a double potential barrier. Families of the modes are constructed in a numerical form, and also by means of the Thomas-Fermi and variation… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.04287v2-abstract-full').style.display = 'inline'; document.getElementById('2104.04287v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2104.04287v2-abstract-full" style="display: none;"> We demonstrate that, with the help of a Gaussian potential barrier, dark modes in the form of a local depression ("bubbles") can be supported by the repulsive Kerr nonlinearity in combination with fractional dimension. Similarly, W-shaped modes are supported by a double potential barrier. Families of the modes are constructed in a numerical form, and also by means of the Thomas-Fermi and variational approximations. All these modes are stable, which is predicted by computation of eigenvalues for small perturbations and confirmed by direct numerical simulations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.04287v2-abstract-full').style.display = 'none'; document.getElementById('2104.04287v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 April, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 9 April, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">to be published in Nonlinear Dynamics</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Nonlinear Dyn. 104(4), 4253-4264 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2101.10212">arXiv:2101.10212</a> <span> [<a href="https://arxiv.org/pdf/2101.10212">pdf</a>, <a href="https://arxiv.org/ps/2101.10212">ps</a>, <a href="https://arxiv.org/format/2101.10212">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevB.103.085111">10.1103/PhysRevB.103.085111 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> External light control of three-dimensional ultrashort far-infrared pulses in an inhomogeneous array of carbon nanotubes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Fedorov%2C+E+G">Eduard G. Fedorov</a>, <a href="/search/?searchtype=author&query=Zhukov%2C+A+V">Alexander V. Zhukov</a>, <a href="/search/?searchtype=author&query=Bouffanais%2C+R">Roland Bouffanais</a>, <a href="/search/?searchtype=author&query=Konobeeva%2C+N+N">Natalia N. Konobeeva</a>, <a href="/search/?searchtype=author&query=Boroznina%2C+E+V">Evgeniya V. Boroznina</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Leblond%2C+H">Herv茅 Leblond</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Belonenko%2C+M+B">Mikhail B. Belonenko</a>, <a href="/search/?searchtype=author&query=Rosanov%2C+N+N">Nikolay N. Rosanov</a>, <a href="/search/?searchtype=author&query=George%2C+T+F">Thomas F. George</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2101.10212v2-abstract-short" style="display: inline;"> We present a study of the propagation of three-dimensional (3D) bipolar electromagnetic ultrashort pulses in an inhomogeneous array of semiconductor carbon nanotubes (CNTs) in the presence of a control high-frequency (HF) electric field. The inhomogeneity is present in the form of a layer with an increased concentration of conduction electrons, which acts as a barrier for the propagation of ultras… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.10212v2-abstract-full').style.display = 'inline'; document.getElementById('2101.10212v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2101.10212v2-abstract-full" style="display: none;"> We present a study of the propagation of three-dimensional (3D) bipolar electromagnetic ultrashort pulses in an inhomogeneous array of semiconductor carbon nanotubes (CNTs) in the presence of a control high-frequency (HF) electric field. The inhomogeneity is present in the form of a layer with an increased concentration of conduction electrons, which acts as a barrier for the propagation of ultrashort electromagnetic pulses through the CNT array. The dynamics of the pulse is described by a nonlinear equation for the vector potential of the electromagnetic field (it takes the form of a 3D generalization of the sine-Gordon equation), derived from the Maxwell's equations and averaged over the period of the HF control field. By means of systematic simulations, we demonstrate that, depending on the amplitude and frequency of the HF control, the ultrashort pulse approaching the barrier layer either passes it or bounces back. The layer's transmissivity for the incident pulse is significantly affected by the amplitude and frequency of the HF control field, with the reflection coefficient nearly vanishing in intervals that make up a discrete set of transparency windows, which resembles the effect of the electromagnetically-induced transparency. Having passed the barrier, the ultrashort pulse continues to propagate, keeping its spatiotemporal integrity. The results may be used for the design of soliton valves, with the transmissivity of the soliton stream accurately controlled by the HF field. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.10212v2-abstract-full').style.display = 'none'; document.getElementById('2101.10212v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">To be published in Phys. Rev. B</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review B 103, no. 8 (2021): 085111 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2012.00694">arXiv:2012.00694</a> <span> [<a href="https://arxiv.org/pdf/2012.00694">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> </div> <p class="title is-5 mathjax"> Propagation dynamics of abruptly autofocusing circular Airy-Gaussian vortex beams in the fractional Schr枚dinger equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=He%2C+S">Shangling He</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Peng%2C+X">Xi Peng</a>, <a href="/search/?searchtype=author&query=Yu%2C+X">Xing Yu</a>, <a href="/search/?searchtype=author&query=He%2C+Y">Yingji He</a>, <a href="/search/?searchtype=author&query=Deng%2C+D">Dongmei Deng</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2012.00694v1-abstract-short" style="display: inline;"> We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical system based on the (2+1)-dimensional fractional Schr枚dinger equation, characterized by its L茅vy index (LI). By means of numerical methods, we explore propagation dynamics of the beams with vorticities from 0 to 4. The propagation leads to abrupt autofocusing, followed by its reversal (rebound from the center). It is sho… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.00694v1-abstract-full').style.display = 'inline'; document.getElementById('2012.00694v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2012.00694v1-abstract-full" style="display: none;"> We introduce axisymmetric Airy-Gaussian vortex beams in a model of an optical system based on the (2+1)-dimensional fractional Schr枚dinger equation, characterized by its L茅vy index (LI). By means of numerical methods, we explore propagation dynamics of the beams with vorticities from 0 to 4. The propagation leads to abrupt autofocusing, followed by its reversal (rebound from the center). It is shown that LI, the relative width of the Airy and Gaussian factors, and the vorticity determine properties of the autofocusing dynamics, including the focusing distance, radius of the focal light spot, and peak intensity at the focus. A maximum of the peak intensity is attained at intermediate values of LI, close to LI=1.4 . Dynamics of the abrupt autofocusing of Airy-Gaussian beams carrying vortex pairs (split double vortices) is considered too. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.00694v1-abstract-full').style.display = 'none'; document.getElementById('2012.00694v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">to be published in Chaos, Solitons & Fractals</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> Article reference: CHAOS_CHAOS-D-20-03626 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> CHAOS 110470 2020 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2010.12748">arXiv:2010.12748</a> <span> [<a href="https://arxiv.org/pdf/2010.12748">pdf</a>, <a href="https://arxiv.org/ps/2010.12748">ps</a>, <a href="https://arxiv.org/format/2010.12748">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1364/OE.409908">10.1364/OE.409908 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Metastable soliton necklaces supported by fractional diffraction and competing nonlinearities </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Li%2C+P">Pengfei Li</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2010.12748v1-abstract-short" style="display: inline;"> We demonstrate that fractional cubic-quintic nonlinear Schr枚dinger equation,characterized by its L茅vy index, maintains ring-shaped soliton clusters ("necklaces") carrying orbital angular momentum. They can be built, in the respective optical setting, as circular chains of fundamental solitons linked by a vortical phase field. We predict semi-analytically that the metastable necklace-shaped cluster… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2010.12748v1-abstract-full').style.display = 'inline'; document.getElementById('2010.12748v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2010.12748v1-abstract-full" style="display: none;"> We demonstrate that fractional cubic-quintic nonlinear Schr枚dinger equation,characterized by its L茅vy index, maintains ring-shaped soliton clusters ("necklaces") carrying orbital angular momentum. They can be built, in the respective optical setting, as circular chains of fundamental solitons linked by a vortical phase field. We predict semi-analytically that the metastable necklace-shaped clusters persist, corresponding to a local minimum of an effective potential of interaction between adjacent solitons in the cluster. Systematic simulations corroborate that the clusters stay robust over extremely large propagation distances, even in the presence of strong random perturbations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2010.12748v1-abstract-full').style.display = 'none'; document.getElementById('2010.12748v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 October, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">To be published in Optics Express</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.07866">arXiv:2008.07866</a> <span> [<a href="https://arxiv.org/pdf/2008.07866">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> </div> <p class="title is-5 mathjax"> Stabilization of single- and multi-peak solitons in the fractional nonlinear Schroedinger equation with a trapping potential </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Qiu%2C+Y">Yunli Qiu</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Zhu%2C+X">Xing Zhu</a>, <a href="/search/?searchtype=author&query=Peng%2C+X">Xi Peng</a>, <a href="/search/?searchtype=author&query=He%2C+Y">Yingji He</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2008.07866v1-abstract-short" style="display: inline;"> We address the existence and stability of localized modes in the framework of the fractional nonlinear Schroedinger equation (FNSE) with the focusing cubic or focusing-defocusing cubic-quintic nonlinearity and a confining harmonic-oscillator (HO) potential. Approximate analytical solutions are obtained in the form of Hermite-Gauss modes. The linear stability analysis and direct simulations reveal… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.07866v1-abstract-full').style.display = 'inline'; document.getElementById('2008.07866v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.07866v1-abstract-full" style="display: none;"> We address the existence and stability of localized modes in the framework of the fractional nonlinear Schroedinger equation (FNSE) with the focusing cubic or focusing-defocusing cubic-quintic nonlinearity and a confining harmonic-oscillator (HO) potential. Approximate analytical solutions are obtained in the form of Hermite-Gauss modes. The linear stability analysis and direct simulations reveal that, under the action of the cubic self-focusing, the single-peak ground state and dipole mode are stabilized by the HO potential at values of the Levy index (the fractionality degree) alpha = 1 and alpha < 1, which lead, respectively, to the critical or supercritical collapse in free space. In addition to that, the inclusion of the quintic self-defocusing provides stabilization of higher-order modes, with the number of local peaks up to seven, at least. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.07866v1-abstract-full').style.display = 'none'; document.getElementById('2008.07866v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">to be published in Chaos, Solitons & Fractals</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2007.12309">arXiv:2007.12309</a> <span> [<a href="https://arxiv.org/pdf/2007.12309">pdf</a>, <a href="https://arxiv.org/format/2007.12309">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s11071-020-05485-x">10.1007/s11071-020-05485-x <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Reductions of the (4 + 1)-dimensional Fokas equation and their solutions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Cao%2C+Y">Yulei Cao</a>, <a href="/search/?searchtype=author&query=He%2C+J">Jingsong He</a>, <a href="/search/?searchtype=author&query=Cheng%2C+Y">Yi Cheng</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2007.12309v2-abstract-short" style="display: inline;"> An integrable extension of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations is investigated in this paper.We will refer to this integrable extension as the (4+1)-dimensional Fokas equation. The determinant expressions of soliton, breather, rational, and semi-rational solutions of the (4 + 1)-dimensional Fokas equation are constructed based on the Hirota's bilinear method and the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.12309v2-abstract-full').style.display = 'inline'; document.getElementById('2007.12309v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2007.12309v2-abstract-full" style="display: none;"> An integrable extension of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations is investigated in this paper.We will refer to this integrable extension as the (4+1)-dimensional Fokas equation. The determinant expressions of soliton, breather, rational, and semi-rational solutions of the (4 + 1)-dimensional Fokas equation are constructed based on the Hirota's bilinear method and the KP hierarchy reduction method. The complex dynamics of these new exact solutions are shown in both three-dimensional plots and two-dimensional contour plots. Interestingly, the patterns of obtained high-order lumps are similar to those of rogue waves in the (1 + 1)-dimensions by choosing different values of the free parameters of the model. Furthermore, three kinds of new semi-rational solutions are presented and the classification of lump fission and fusion processes is also discussed. Additionally, we give a new way to obtain rational and semi-rational solutions of (3 + 1)-dimensional KP equation by reducing the solutions of the (4 + 1)-dimensional Fokas equation. All these results show that the (4 + 1)-dimensional Fokas equation is a meaningful multidimensional extension of the KP and DS equations. The obtained results might be useful in diverse fields such as hydrodynamics, non-linear optics and photonics, ion-acoustic waves in plasmas, matter waves in Bose-Einstein condensates, and sound waves in ferromagnetic media. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.12309v2-abstract-full').style.display = 'none'; document.getElementById('2007.12309v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Nonlinear Dynamics, 99, (2020) 3013-3028</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.14161">arXiv:2003.14161</a> <span> [<a href="https://arxiv.org/pdf/2003.14161">pdf</a>, <a href="https://arxiv.org/ps/2003.14161">ps</a>, <a href="https://arxiv.org/format/2003.14161">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.chaos.2020.109602">10.1016/j.chaos.2020.109602 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Symmetry breaking of spatial Kerr solitons in fractional dimension </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Li%2C+P">Pengfei Li</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2003.14161v1-abstract-short" style="display: inline;"> We study symmetry breaking of solitons in the framework of a nonlinear fractional Schr枚dinger equation (NLFSE), characterized by its L茅vy index, with cubic nonlinearity and a symmetric double-well potential. Asymmetric, symmetric, and antisymmetric soliton solutions are found, with stable asymmetric soliton solutions emerging from unstable symmetric and antisymmetric ones by way of symmetry-breaki… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.14161v1-abstract-full').style.display = 'inline'; document.getElementById('2003.14161v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2003.14161v1-abstract-full" style="display: none;"> We study symmetry breaking of solitons in the framework of a nonlinear fractional Schr枚dinger equation (NLFSE), characterized by its L茅vy index, with cubic nonlinearity and a symmetric double-well potential. Asymmetric, symmetric, and antisymmetric soliton solutions are found, with stable asymmetric soliton solutions emerging from unstable symmetric and antisymmetric ones by way of symmetry-breaking bifurcations. Two different bifurcation scenarios are possible. First, symmetric soliton solutions undergo a symmetry-breaking bifurcation of the pitchfork type, which gives rise to a branch of asymmetric solitons, under the action of the self-focusing nonlinearity. Second, a family of asymmetric solutions branches off from antisymmetric states in the case of self-defocusing nonlinearity through a bifurcation of an inverted-pitchfork type. Systematic numerical analysis demonstrates that increase of the L茅vy index leads to shrinkage or expansion of the symmetry-breaking region, depending on parameters of the double-well potential. Stability of the soliton solutions is explored following the variation of the L茅vy index, and the results are confirmed by direct numerical simulations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.14161v1-abstract-full').style.display = 'none'; document.getElementById('2003.14161v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 March, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 12 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2003.14137">arXiv:2003.14137</a> <span> [<a href="https://arxiv.org/pdf/2003.14137">pdf</a>, <a href="https://arxiv.org/ps/2003.14137">ps</a>, <a href="https://arxiv.org/format/2003.14137">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> </div> <p class="title is-5 mathjax"> Vortex solitons in fractional nonlinear Schr枚dinger equation with the cubic-quintic nonlinearity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Li%2C+P">Pengfei Li</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2003.14137v1-abstract-short" style="display: inline;"> We address the existence and stability of vortex-soliton (VS) solutions of the fractional nonlinear Schr枚dinger equation (NLSE) with competing cubic-quintic nonlinearities and the L茅vy index (fractionality) taking values 1 \leq伪\leq2. Families of ring-shaped VSs with vorticities s = 1,2, and 3 are constructed in a numerical form. Unlike the usual two-dimensional NLSE (which corresponds to 伪 = 2),… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.14137v1-abstract-full').style.display = 'inline'; document.getElementById('2003.14137v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2003.14137v1-abstract-full" style="display: none;"> We address the existence and stability of vortex-soliton (VS) solutions of the fractional nonlinear Schr枚dinger equation (NLSE) with competing cubic-quintic nonlinearities and the L茅vy index (fractionality) taking values 1 \leq伪\leq2. Families of ring-shaped VSs with vorticities s = 1,2, and 3 are constructed in a numerical form. Unlike the usual two-dimensional NLSE (which corresponds to 伪 = 2), in the fractional model VSs exist above a finite threshold value of the total power,P. Stability of the VS solutions is investigated for small perturbations governed by the linearized equation, and corroborated by direct simulations. Unstable VSs are broken up by azimuthal perturbations into several fragments, whose number is determined by the fastest growing eigenmode of small perturbations. The stability region, defined in terms of P, expands with the increase of 伪 from 1 up to 2 for all s = 1, 2, and 3, except for steep shrinkage for s = 2 in the interval of 1\leq伪\leq1.3. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2003.14137v1-abstract-full').style.display = 'none'; document.getElementById('2003.14137v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 March, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">23 pages, 8 figures, to be published in Chaos, Solitons & Fractals"</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1910.04370">arXiv:1910.04370</a> <span> [<a href="https://arxiv.org/pdf/1910.04370">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.chaos.2019.109471">10.1016/j.chaos.2019.109471 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Soliton dynamics in a fractional complex Ginzburg-Landau model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Qiu%2C+Y">Yunli Qiu</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Zhu%2C+X">Xing Zhu</a>, <a href="/search/?searchtype=author&query=Zhang%2C+L">Li Zhang</a>, <a href="/search/?searchtype=author&query=He%2C+Y">Yingji He</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1910.04370v1-abstract-short" style="display: inline;"> The general objective of the work is to study dynamics of dissipative solitons in the framework of a one-dimensional complex Ginzburg-Landau equation (CGLE) of a fractional order. To estimate the shape of solitons in fractional models, we first develop the variational approximation for solitons of the fractional nonlinear Schrodinger equation (NLSE), and an analytical approximation for exponential… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.04370v1-abstract-full').style.display = 'inline'; document.getElementById('1910.04370v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1910.04370v1-abstract-full" style="display: none;"> The general objective of the work is to study dynamics of dissipative solitons in the framework of a one-dimensional complex Ginzburg-Landau equation (CGLE) of a fractional order. To estimate the shape of solitons in fractional models, we first develop the variational approximation for solitons of the fractional nonlinear Schrodinger equation (NLSE), and an analytical approximation for exponentially decaying tails of the solitons. Proceeding to numerical consideration of solitons in fractional CGLE, we study, in necessary detail, effects of the respective Levy index (LI) on the solitons' dynamics. In particular, dependence of stability domains in the model's parameter space on the LI is identified. Pairs of in-phase dissipative solitons merge into single pulses, with the respective merger distance also determined by LI. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.04370v1-abstract-full').style.display = 'none'; document.getElementById('1910.04370v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 October, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">To be published on Chaos, Solitons & Fractals</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1909.00118">arXiv:1909.00118</a> <span> [<a href="https://arxiv.org/pdf/1909.00118">pdf</a>, <a href="https://arxiv.org/ps/1909.00118">ps</a>, <a href="https://arxiv.org/format/1909.00118">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1364/OE.27.027592">10.1364/OE.27.027592 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Asymptotic dynamics of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Fedorov%2C+E+G">Eduard G. Fedorov</a>, <a href="/search/?searchtype=author&query=Zhukov%2C+A+V">Alexander V. Zhukov</a>, <a href="/search/?searchtype=author&query=Bouffanais%2C+R">Roland Bouffanais</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Leblond%2C+H">Herv茅 Leblond</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Rosanov%2C+N+N">Nikolay N. Rosanov</a>, <a href="/search/?searchtype=author&query=Belonenko%2C+M+B">Mikhail B. Belonenko</a>, <a href="/search/?searchtype=author&query=George%2C+T+F">Thomas F. George</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1909.00118v2-abstract-short" style="display: inline;"> We study the propagation of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes at times much longer than the pulse duration, yet still shorter than the relaxation time in the system. The interaction of the electromagnetic field with the electronic subsystem of the medium is described by means of Maxwell's equations, taking into account the fie… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.00118v2-abstract-full').style.display = 'inline'; document.getElementById('1909.00118v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1909.00118v2-abstract-full" style="display: none;"> We study the propagation of three-dimensional bipolar ultrashort electromagnetic pulses in an array of semiconductor carbon nanotubes at times much longer than the pulse duration, yet still shorter than the relaxation time in the system. The interaction of the electromagnetic field with the electronic subsystem of the medium is described by means of Maxwell's equations, taking into account the field inhomogeneity along the nanotube axis beyond the approximation of slowly varying amplitudes and phases. A model is proposed for the analysis of the dynamics of an electromagnetic pulse in the form of an effective equation for the vector potential of the field. Our numerical analysis demonstrates the possibility of a satisfactory description of the evolution of the pulse field at large times by means of a three-dimensional generalization of the sine-Gordon and double sine-Gordon equations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1909.00118v2-abstract-full').style.display = 'none'; document.getElementById('1909.00118v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">To Appear in Optics Express</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Opt. Exp., (27), 27592, 2019 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1905.04658">arXiv:1905.04658</a> <span> [<a href="https://arxiv.org/pdf/1905.04658">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.physleta.2019.05.022">10.1016/j.physleta.2019.05.022 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Generation of stable multi-vortex clusters in a dissipative medium with anti-cubic nonlinearity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Qiu%2C+Y">Y. Qiu</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">B. A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">D. Mihalache</a>, <a href="/search/?searchtype=author&query=Zhu%2C+X">X. Zhu</a>, <a href="/search/?searchtype=author&query=Peng%2C+J">J. Peng</a>, <a href="/search/?searchtype=author&query=He%2C+Y">Y. He</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1905.04658v1-abstract-short" style="display: inline;"> We demonstrate the generation of vortex solitons in a model of dissipative optical media with the singular anti-cubic (AC) nonlinearity, by launching a vorticity-carrying Gaussian input into the medium modeled by the cubic-quintic complex Ginzburg-Landau equation with the additional AC term. The effect of the latter term on the beam propagation is investigated in detail. An analytical result is pr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.04658v1-abstract-full').style.display = 'inline'; document.getElementById('1905.04658v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1905.04658v1-abstract-full" style="display: none;"> We demonstrate the generation of vortex solitons in a model of dissipative optical media with the singular anti-cubic (AC) nonlinearity, by launching a vorticity-carrying Gaussian input into the medium modeled by the cubic-quintic complex Ginzburg-Landau equation with the additional AC term. The effect of the latter term on the beam propagation is investigated in detail. An analytical result is produced for the asymptotic form of fundamental and vortical solitons at r --> 0, which is determined by the AC term. Numerical simulations identify parameter domains which maintain stable dissipative solitons in the form of vortex clusters. The number of vortices in the clusters is equal to the vorticity embedded in the Gaussian input. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1905.04658v1-abstract-full').style.display = 'none'; document.getElementById('1905.04658v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 May, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">to be published in Physics Letters A</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1805.08444">arXiv:1805.08444</a> <span> [<a href="https://arxiv.org/pdf/1805.08444">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> Generation of ring-shaped optical vortices in dissipative media by inhomogeneous effective diffusion </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Lai%2C+S">Shiquan Lai</a>, <a href="/search/?searchtype=author&query=Li%2C+H">Huishan Li</a>, <a href="/search/?searchtype=author&query=Qui%2C+Y">Yunli Qui</a>, <a href="/search/?searchtype=author&query=Zhu%2C+X">Xing Zhu</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=He%2C+Y">Yingji He</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1805.08444v1-abstract-short" style="display: inline;"> By means of systematic simulations we demonstrate generation of a variety of ring-shaped optical vortices (OVs) from a two-dimensional input with embedded vorticity, in a dissipative medium modeled by the cubic-quintic complex Ginzburg-Landau equation with an inhomogeneous effective diffusion (spatial-filtering) term, which is anisotropic in the transverse plane and periodically modulated in the l… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1805.08444v1-abstract-full').style.display = 'inline'; document.getElementById('1805.08444v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1805.08444v1-abstract-full" style="display: none;"> By means of systematic simulations we demonstrate generation of a variety of ring-shaped optical vortices (OVs) from a two-dimensional input with embedded vorticity, in a dissipative medium modeled by the cubic-quintic complex Ginzburg-Landau equation with an inhomogeneous effective diffusion (spatial-filtering) term, which is anisotropic in the transverse plane and periodically modulated in the longitudinal direction. We show the generation of stable square- and gear-shaped OVs, as well as tilted oval-shaped vortex rings, and string-shaped bound states built of a central fundamental soliton and two vortex satellites, or of three fundamental solitons. Their shape can be adjusted by tuning the strength and modulation period of the inhomogeneous diffusion. Stability domains of the generated OVs are identified by varying the vorticity of the input and parameters of the inhomogeneous diffusion. The results suggest a method to generate new types of ring-shaped OVs with applications to the work with structured light. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1805.08444v1-abstract-full').style.display = 'none'; document.getElementById('1805.08444v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 May, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages, 5 figures; Nonlinear Dynamics, in press</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1804.03314">arXiv:1804.03314</a> <span> [<a href="https://arxiv.org/pdf/1804.03314">pdf</a>, <a href="https://arxiv.org/ps/1804.03314">ps</a>, <a href="https://arxiv.org/format/1804.03314">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1098/rsta.2017.0378">10.1098/rsta.2017.0378 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Li%2C+P">Pengfei Li</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1804.03314v1-abstract-short" style="display: inline;"> We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.03314v1-abstract-full').style.display = 'inline'; document.getElementById('1804.03314v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1804.03314v1-abstract-full" style="display: none;"> We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such PT -symmetric waveguides. The dependence of the propagation constant on the soliton's power is presented for different strengths of the nonlinearity saturation, S. The stability of fundamental, dipole, tripole, and quadrupole solitons is investigated by means of the linear-stability analysis and direct numerical simulations of the corresponding (1+1)-dimensional nonlinear Schrodinger-type equation. The results show that the instability of the stationary solutions can be mitigated or completely suppressed, increasing the value of S. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.03314v1-abstract-full').style.display = 'none'; document.getElementById('1804.03314v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 April, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, 6 figures, Phil. Trans. Roy. Soc. A, in press ( a theme issue on "Dissipative Structures in Matter out of Equilibrium: From Chemistry, Photonics and Biology", ed. by M. Tlidi, M. Clerc, and K. Panaiotov)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1804.02629">arXiv:1804.02629</a> <span> [<a href="https://arxiv.org/pdf/1804.02629">pdf</a>, <a href="https://arxiv.org/ps/1804.02629">ps</a>, <a href="https://arxiv.org/format/1804.02629">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> Optical Solitons in PT-symmetric Potentials with Competing Cubic-Quintic Nonlinearity: Existence, Stability, and Dynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Li%2C+P">Pengfei Li</a>, <a href="/search/?searchtype=author&query=Li%2C+L">Lu Li</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1804.02629v1-abstract-short" style="display: inline;"> We address the properties of optical solitons that form in media with competing cubic-quintic nonlinearity and parity-time(PT)-symmetric complex-valued external potentials. The model describes the propagation of solitons in nonlinear optical waveguides with balanced gain and loss. We study the existence, stability, and robustness of fundamental, dipole, and multipole stationary solutions in this P… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.02629v1-abstract-full').style.display = 'inline'; document.getElementById('1804.02629v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1804.02629v1-abstract-full" style="display: none;"> We address the properties of optical solitons that form in media with competing cubic-quintic nonlinearity and parity-time(PT)-symmetric complex-valued external potentials. The model describes the propagation of solitons in nonlinear optical waveguides with balanced gain and loss. We study the existence, stability, and robustness of fundamental, dipole, and multipole stationary solutions in this PT-symmetric system. The corresponding eigenvalue spectra diagrams for fundamental, dipole, tripole, and quadrupole solitons are presented. We show that the eigenvalue spectra diagrams for fundamental and dipole solitons merge at a coalescence point Wc1, whereas the corresponding diagrams for tripole and quadrupole solitons merge at a larger coalescence point Wc2. Beyond these two merging points, i.e., when the gain-loss strength parameter W0 exceeds the corresponding coalescence points, the eigenvalue spectra cease to exist. The stability of the stationary solutions is investigated by performing the linear stability analysis and the robustness to propagation of these stationary solutions is checked by using direct numerical simulations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.02629v1-abstract-full').style.display = 'none'; document.getElementById('1804.02629v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 April, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 5 figures,published in Rom. Rep. Phys. 70, 408 (2018)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1804.01643">arXiv:1804.01643</a> <span> [<a href="https://arxiv.org/pdf/1804.01643">pdf</a>, <a href="https://arxiv.org/ps/1804.01643">ps</a>, <a href="https://arxiv.org/format/1804.01643">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.97.043814">10.1103/PhysRevA.97.043814 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Propagation of three-dimensional bipolar ultrashort electromagnetic pulses in an inhomogeneous array of carbon nanotubes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Fedorov%2C+E+G">Eduard G. Fedorov</a>, <a href="/search/?searchtype=author&query=Zhukov%2C+A+V">Alexander V. Zhukov</a>, <a href="/search/?searchtype=author&query=Bouffanais%2C+R">Roland Bouffanais</a>, <a href="/search/?searchtype=author&query=Timashkov%2C+A+P">Alexander P. Timashkov</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Leblond%2C+H">Herv茅 Leblond</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Rosanov%2C+N+N">Nikolay N. Rosanov</a>, <a href="/search/?searchtype=author&query=Belonenko%2C+M+B">Mikhail B. Belonenko</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1804.01643v1-abstract-short" style="display: inline;"> We study the propagation of three-dimensional (3D) bipolar ultrashort electromagnetic pulses in an inhomogeneous array of semiconductor carbon nanotubes. The heterogeneity is represented by a planar region with an increased concentration of conduction electrons. The evolution of the electromagnetic field and electron concentration in the sample are governed by the Maxwell's equations and continuit… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.01643v1-abstract-full').style.display = 'inline'; document.getElementById('1804.01643v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1804.01643v1-abstract-full" style="display: none;"> We study the propagation of three-dimensional (3D) bipolar ultrashort electromagnetic pulses in an inhomogeneous array of semiconductor carbon nanotubes. The heterogeneity is represented by a planar region with an increased concentration of conduction electrons. The evolution of the electromagnetic field and electron concentration in the sample are governed by the Maxwell's equations and continuity equation. In particular, non-uniformity of the electromagnetic field along the axis of the nanotubes is taken into account. We demonstrate that, depending on values of parameters of the electromagnetic pulse approaching the region with the higher electron concentration, the pulse is reflected from the region or passes it. Specifically, our simulations demonstrate that, after interacting with the higher-concentration area, the pulse can propagate steadily, without significant spreading. The possibility of such ultrashort electromagnetic pulses propagating in arrays of carbon nanotubes over distances significantly exceeding characteristic dimensions of the pulses makes it possible to consider them as 3D solitons. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.01643v1-abstract-full').style.display = 'none'; document.getElementById('1804.01643v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 April, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Phys. Rev. A, In Press</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 97 (2018) 043814 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1712.10013">arXiv:1712.10013</a> <span> [<a href="https://arxiv.org/pdf/1712.10013">pdf</a>, <a href="https://arxiv.org/format/1712.10013">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> </div> </div> <p class="title is-5 mathjax"> Semi-rational solutions for the (2 + 1)-dimensional nonlocal Fokas system </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Cao%2C+Y">Yulei Cao</a>, <a href="/search/?searchtype=author&query=Rao%2C+J">Jiguang Rao</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=He%2C+J">Jingsong He</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1712.10013v2-abstract-short" style="display: inline;"> The (2+1)-dimensional [(2+1)d] Fokas system is a natural and simple extension of the nonlinear Schrodinger equation. (see eq. (2) in A. S. Fokas, Inverse Probl. 10 (1994) L19-L22). In this letter, we introduce its PT -symmetric version, which is called the (2 + 1)d nonlocal Fokas system. The N-soliton solutions for this system are obtained by using the Hirota bilinear method whereas the semi-ratio… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.10013v2-abstract-full').style.display = 'inline'; document.getElementById('1712.10013v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1712.10013v2-abstract-full" style="display: none;"> The (2+1)-dimensional [(2+1)d] Fokas system is a natural and simple extension of the nonlinear Schrodinger equation. (see eq. (2) in A. S. Fokas, Inverse Probl. 10 (1994) L19-L22). In this letter, we introduce its PT -symmetric version, which is called the (2 + 1)d nonlocal Fokas system. The N-soliton solutions for this system are obtained by using the Hirota bilinear method whereas the semi-rational solutions are generated by taking the long-wave limit of a part of exponential functions in the general expression of the N-soliton solution. Three kinds of semi-rational solutions, namely (1) a hybrid of rogue waves and periodic line waves, (2) a hybrid of lump and breather solutions, and (3) a hybrid of lump, breather, and periodic line waves are put forward and their rather complicated dynamics is revealed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.10013v2-abstract-full').style.display = 'none'; document.getElementById('1712.10013v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 January, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 December, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted by Applied Mathematics Letters, 7 pages including 5 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1712.08718">arXiv:1712.08718</a> <span> [<a href="https://arxiv.org/pdf/1712.08718">pdf</a>, <a href="https://arxiv.org/format/1712.08718">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Families of exact solutions of a new extended (2+1)-dimensional Boussinesq equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Cao%2C+Y">Yulei Cao</a>, <a href="/search/?searchtype=author&query=He%2C+J">Jingsong He</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1712.08718v1-abstract-short" style="display: inline;"> A new variant of the $(2+1)$-dimensional [$(2+1)d$] Boussinesq equation was recently introduced by J. Y. Zhu, arxiv:1704.02779v2, 2017; see eq. (3). First, we derive in this paper the one-soliton solutions of both bright and dark types for the extended $(2+1)d$ Boussinesq equation by using the traveling wave method. Second, $N$-soliton, breather, and rational solutions are obtained by using the Hi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.08718v1-abstract-full').style.display = 'inline'; document.getElementById('1712.08718v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1712.08718v1-abstract-full" style="display: none;"> A new variant of the $(2+1)$-dimensional [$(2+1)d$] Boussinesq equation was recently introduced by J. Y. Zhu, arxiv:1704.02779v2, 2017; see eq. (3). First, we derive in this paper the one-soliton solutions of both bright and dark types for the extended $(2+1)d$ Boussinesq equation by using the traveling wave method. Second, $N$-soliton, breather, and rational solutions are obtained by using the Hirota bilinear method and the long wave limit. Nonsingular rational solutions of two types were obtained analytically, namely: (i) rogue-wave solutions having the form of W-shaped lines waves and (ii) lump-type solutions. Two generic types of semi-rational solutions were also put forward. The obtained semi-rational solutions are as follows: (iii) a hybrid of a first-order lump and a bright one-soliton solution and (iv) a hybrid of a first-order lump and a first-order breather. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.08718v1-abstract-full').style.display = 'none'; document.getElementById('1712.08718v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 December, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Accepted by Nonlinear Dynamics, 19 pages including 10 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.06836">arXiv:1705.06836</a> <span> [<a href="https://arxiv.org/pdf/1705.06836">pdf</a>, <a href="https://arxiv.org/ps/1705.06836">ps</a>, <a href="https://arxiv.org/format/1705.06836">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> </div> <p class="title is-5 mathjax"> Smooth positon solutions of the focusing modified Korteweg-de Vries equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Xing%2C+Q">Qiuxia Xing</a>, <a href="/search/?searchtype=author&query=Wu%2C+Z">Zhiwei Wu</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=He%2C+J">Jingsong He</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.06836v1-abstract-short" style="display: inline;"> The $n$-fold Darboux transformation $T_{n}$ of the focusing real mo\-di\-fied Kor\-te\-weg-de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the $n$-soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the eigenvalues $位_{j}$ and the corresponding eigenfunctions of the associated Lax equation.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.06836v1-abstract-full').style.display = 'inline'; document.getElementById('1705.06836v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.06836v1-abstract-full" style="display: none;"> The $n$-fold Darboux transformation $T_{n}$ of the focusing real mo\-di\-fied Kor\-te\-weg-de Vries (mKdV) equation is expressed in terms of the determinant representation. Using this representation, the $n$-soliton solutions of the mKdV equation are also expressed by determinants whose elements consist of the eigenvalues $位_{j}$ and the corresponding eigenfunctions of the associated Lax equation. The nonsingular $n$-positon solutions of the focusing mKdV equation are obtained in the special limit $位_{j}\rightarrow位_{1}$, from the corresponding $n$-soliton solutions and by using the associated higher-order Taylor expansion. Furthermore, the decomposition method of the $n$-positon solution into $n$ single-soliton solutions, the trajectories, and the corresponding "phase shifts" of the multi-positons are also investigated. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.06836v1-abstract-full').style.display = 'none'; document.getElementById('1705.06836v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages, 7 figures. This is the accepted version by Nonlinear Dynamics</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1704.05599">arXiv:1704.05599</a> <span> [<a href="https://arxiv.org/pdf/1704.05599">pdf</a>, <a href="https://arxiv.org/format/1704.05599">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Exactly Solvable and Integrable Systems">nlin.SI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1063/1.4982721">10.1063/1.4982721 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Construction of rational solutions of the real modified Korteweg-de Vries equation from its periodic solutions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Xing%2C+Q">Qiuxia Xing</a>, <a href="/search/?searchtype=author&query=Wang%2C+L">Lihong Wang</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Porsezian%2C+K">Kappuswamy Porsezian</a>, <a href="/search/?searchtype=author&query=He%2C+J">Jingsong He</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1704.05599v1-abstract-short" style="display: inline;"> In this paper, we consider the real modified Korteweg-de Vries (mKdV) equation and construct a special kind of breather solution, which can be obtained by taking the limit $位_{j}$ $\rightarrow$ $位_{1}$ of the Lax pair eigenvalues used in the $n$-fold Darboux transformation that generates the order-$n$ periodic solution from a constant seed solution. Further, this special kind of breather solution… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1704.05599v1-abstract-full').style.display = 'inline'; document.getElementById('1704.05599v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1704.05599v1-abstract-full" style="display: none;"> In this paper, we consider the real modified Korteweg-de Vries (mKdV) equation and construct a special kind of breather solution, which can be obtained by taking the limit $位_{j}$ $\rightarrow$ $位_{1}$ of the Lax pair eigenvalues used in the $n$-fold Darboux transformation that generates the order-$n$ periodic solution from a constant seed solution. Further, this special kind of breather solution of order $n$ can be used to generate the order-$n$ rational solution by taking the limit $位_{1}$ $\rightarrow$ $位_{0}$, where $位_{0}$ is a special eigenvalue associated to the eigenfunction $蠁$ of the Lax pair of the mKdV equation. This eigenvalue $位_0$, for which $蠁(位_0)=0$, corresponds to the limit of infinite period of the periodic solution. %This second limit of double eigenvalue degeneration might be realized approximately in optical fibers, in which an injected %initial ideal pulse is created by a comb system and a programmable optical filter according to the profile of the analytical %form of the b-positon at a certain spatial position $x_{0}$. Therefore, we suggest a new way to observe the higher-order %rational solutions in optical fibers, namely, to measure the wave patterns at the central region of the higher order b-positon %generated by ideal initial pulses when the eigenvalue $位_{1}$ is approaching $位_{0}$. Our analytical and numerical results show the effective mechanism of generation of higher-order rational solutions of the mKdV equation from the double eigenvalue degeneration process of multi-periodic solutions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1704.05599v1-abstract-full').style.display = 'none'; document.getElementById('1704.05599v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 April, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22pages, 9 figures. This is the accepted version by Chaos</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1703.10466">arXiv:1703.10466</a> <span> [<a href="https://arxiv.org/pdf/1703.10466">pdf</a>, <a href="https://arxiv.org/ps/1703.10466">ps</a>, <a href="https://arxiv.org/format/1703.10466">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Physics">quant-ph</span> </div> </div> <p class="title is-5 mathjax"> Families of stable solitons and excitations in the PT-symmetric nonlinear Schrodinger equations with position-dependent effective masses </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Chen%2C+Y">Yong Chen</a>, <a href="/search/?searchtype=author&query=Yan%2C+Z">Zhenya Yan</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1703.10466v1-abstract-short" style="display: inline;"> Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1703.10466v1-abstract-full').style.display = 'inline'; document.getElementById('1703.10466v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1703.10466v1-abstract-full" style="display: none;"> Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $\mathcal{PT}$-symmetric Scarf-II potentials. The broken linear PT symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than PT-symmetric ones, but feature similar properties. Our results may suggest new experiments for PT-symmetric nonlinear waves in nonlinear nonuniform optical media. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1703.10466v1-abstract-full').style.display = 'none'; document.getElementById('1703.10466v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 March, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 14 figures (Scientific Reports, in press)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Scientific Reports 7 (2017) 1257 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1610.08338">arXiv:1610.08338</a> <span> [<a href="https://arxiv.org/pdf/1610.08338">pdf</a>, <a href="https://arxiv.org/ps/1610.08338">ps</a>, <a href="https://arxiv.org/format/1610.08338">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.94.053823">10.1103/PhysRevA.94.053823 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Collisions of three-dimensional bipolar optical solitons in an array of carbon nanotubes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Zhukov%2C+A+V">Alexander V. Zhukov</a>, <a href="/search/?searchtype=author&query=Bouffanais%2C+R">Roland Bouffanais</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Leblond%2C+H">Herv茅 Leblond</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Fedorov%2C+E+G">Eduard G. Fedorov</a>, <a href="/search/?searchtype=author&query=Rosanov%2C+N+N">Nikolay N. Rosanov</a>, <a href="/search/?searchtype=author&query=Belonenko%2C+M+B">Mikhail B. Belonenko</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1610.08338v2-abstract-short" style="display: inline;"> We study interactions of extremely short three-dimensional bipolar electromagnetic pulses propagating towards each other in an array of semiconductor carbon nanotubes, along any direction perpendicular to their axes. The analysis provides a full account of the effects of the nonuniformity of the pulses' fields along the axes. The evolution of the electromagnetic field and charge density in the sam… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1610.08338v2-abstract-full').style.display = 'inline'; document.getElementById('1610.08338v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1610.08338v2-abstract-full" style="display: none;"> We study interactions of extremely short three-dimensional bipolar electromagnetic pulses propagating towards each other in an array of semiconductor carbon nanotubes, along any direction perpendicular to their axes. The analysis provides a full account of the effects of the nonuniformity of the pulses' fields along the axes. The evolution of the electromagnetic field and charge density in the sample is derived from the Maxwell's equations and the continuity equation, respectively. In particular, we focus on indirect interaction of the pulses via the action of their fields on the electronic subsystem of the nanotube array. Changes in the shape of pulses in the course of their propagation and interaction are analyzed by calculating and visualizing the distribution of the electric field in the system. The numerical analysis reveals a possibility of stable post-collision propagation of pulses over distances much greater than their sizes. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1610.08338v2-abstract-full').style.display = 'none'; document.getElementById('1610.08338v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. A 94 (2016) 053823 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1603.04756">arXiv:1603.04756</a> <span> [<a href="https://arxiv.org/pdf/1603.04756">pdf</a>, <a href="https://arxiv.org/ps/1603.04756">ps</a>, <a href="https://arxiv.org/format/1603.04756">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> Commentary (invited update) to article "Spatiotemporal optical solitons", by B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclass. Opt. 7, R53-R72 (2005) </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Wise%2C+F">Frank Wise</a>, <a href="/search/?searchtype=author&query=Torner%2C+L">Lluis Torner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1603.04756v1-abstract-short" style="display: inline;"> This is an invited short update of the topic covered by the review article, which aims to briefly survey progress made in theoretical and experimental studies of multidimensional solitons since the publication of the review. The Commentary was invited as an addition to the original review article that will be reprinted in an e-book celebrating the 50th anniversary of Journal of Physics B (incorpor… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1603.04756v1-abstract-full').style.display = 'inline'; document.getElementById('1603.04756v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1603.04756v1-abstract-full" style="display: none;"> This is an invited short update of the topic covered by the review article, which aims to briefly survey progress made in theoretical and experimental studies of multidimensional solitons since the publication of the review. The Commentary was invited as an addition to the original review article that will be reprinted in an e-book celebrating the 50th anniversary of Journal of Physics B (incorporating Journal of Optics B: Quantum and Semiclassical Optics). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1603.04756v1-abstract-full').style.display = 'none'; document.getElementById('1603.04756v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 March, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2016. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1502.06328">arXiv:1502.06328</a> <span> [<a href="https://arxiv.org/pdf/1502.06328">pdf</a>, <a href="https://arxiv.org/ps/1502.06328">ps</a>, <a href="https://arxiv.org/format/1502.06328">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Gases">cond-mat.quant-gas</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Atomic Physics">physics.atom-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computational Physics">physics.comp-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> </div> <p class="title is-5 mathjax"> Bose-Einstein condensation: Twenty years after </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Bagnato%2C+V+S">V. S. Bagnato</a>, <a href="/search/?searchtype=author&query=Frantzeskakis%2C+D+J">D. J. Frantzeskakis</a>, <a href="/search/?searchtype=author&query=Kevrekidis%2C+P+G">P. G. Kevrekidis</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">B. A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">D. Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1502.06328v1-abstract-short" style="display: inline;"> The aim of this introductory article is two-fold. First, we aim to offer a general introduction to the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of relevant research directions during the last two decades. Second, we introduce and present the articles that appear in this Special Volume of Romanian Reports in Physics celebrating the conclusion of the second d… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1502.06328v1-abstract-full').style.display = 'inline'; document.getElementById('1502.06328v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1502.06328v1-abstract-full" style="display: none;"> The aim of this introductory article is two-fold. First, we aim to offer a general introduction to the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of relevant research directions during the last two decades. Second, we introduce and present the articles that appear in this Special Volume of Romanian Reports in Physics celebrating the conclusion of the second decade since the experimental creation of Bose-Einstein condensation in ultracold gases of alkali-metal atoms. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1502.06328v1-abstract-full').style.display = 'none'; document.getElementById('1502.06328v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 February, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Special Volume of Romanian Reports in Physics dedicated to Bose-Einstein condensation</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Rom. Rep. Phys. 67, 5-50 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1411.7833">arXiv:1411.7833</a> <span> [<a href="https://arxiv.org/pdf/1411.7833">pdf</a>, <a href="https://arxiv.org/ps/1411.7833">ps</a>, <a href="https://arxiv.org/format/1411.7833">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.90.062909">10.1103/PhysRevE.90.062909 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Breather-like solitons extracted from the Peregrine rogue wave </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Yang%2C+G">Guangye Yang</a>, <a href="/search/?searchtype=author&query=Wang%2C+Y">Yan Wang</a>, <a href="/search/?searchtype=author&query=Qin%2C+Z">Zhenyun Qin</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Li%2C+L">Lu Li</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1411.7833v1-abstract-short" style="display: inline;"> Based on the Peregrine solution (PS) of the nonlinear Schr枚dinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breather-like solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realis… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1411.7833v1-abstract-full').style.display = 'inline'; document.getElementById('1411.7833v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1411.7833v1-abstract-full" style="display: none;"> Based on the Peregrine solution (PS) of the nonlinear Schr枚dinger (NLS) equation, the evolution of rational fraction pulses surrounded by zero background is investigated. These pulses display the behavior of a breather-like solitons. We study the generation and evolution of such solitons extracted, by means of the spectral-filtering method, from the PS in the model of the optical fiber with realistic values of coefficients accounting for the anomalous dispersion, Kerr nonlinearity, and higher-order effects. The results demonstrate that the breathing solitons stably propagate in the fibers. Their robustness against small random perturbations applied to the initial background is demonstrated too. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1411.7833v1-abstract-full').style.display = 'none'; document.getElementById('1411.7833v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 November, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 8 figures, Phys.Rev.E, in press</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys.Rev.E.90.062909(2014) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1403.5436">arXiv:1403.5436</a> <span> [<a href="https://arxiv.org/pdf/1403.5436">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1098/rsta.2014.0017">10.1098/rsta.2014.0017 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Localized modes in dissipative lattice media: An overview </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=He%2C+Y">Yingji He</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1403.5436v1-abstract-short" style="display: inline;"> We overview recent theoretical studies of the dynamics of one- and two-dimensional spatial dissipative solitons in models based on the complex Ginzburg-Landau equations with the cubic-quintic combination of loss and gain terms, which include imaginary, real, or complex spatially periodic potentials. The imaginary potential represents periodic modulation of the local loss and gain. It is shown that… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1403.5436v1-abstract-full').style.display = 'inline'; document.getElementById('1403.5436v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1403.5436v1-abstract-full" style="display: none;"> We overview recent theoretical studies of the dynamics of one- and two-dimensional spatial dissipative solitons in models based on the complex Ginzburg-Landau equations with the cubic-quintic combination of loss and gain terms, which include imaginary, real, or complex spatially periodic potentials. The imaginary potential represents periodic modulation of the local loss and gain. It is shown that the effective gradient force, induced by the inhomogeneous loss distribution, gives rise to three generic propagation scenarios for one-dimensional (1D) dissipative solitons: transverse drift, persistent swing motion, and damped oscillations. When the lattice-average loss/gain value is zero, and the real potential has spatial parity opposite to that of the imaginary component, the respective complex potential is a realization of the parity-time symmetry. Under the action of lattice potentials of the latter type, 1D solitons feature unique motion regimes in the form of transverse drift and persistent swing. In the 2D geometry, three types of axisymmetric radial lattices are considered, viz., ones based solely on the refractive-index modulation, or solely on the linear-loss modulation, or on a combination of both. The rotary motion of solitons in such axisymmetric potentials can be effectively controlled by varying the strength of the initial tangential kick. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1403.5436v1-abstract-full').style.display = 'none'; document.getElementById('1403.5436v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 March, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2014. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Philosophical Transactions of the Royal Society A, in press(Special Issue "Localized structures in dissipative media")</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1307.4333">arXiv:1307.4333</a> <span> [<a href="https://arxiv.org/pdf/1307.4333">pdf</a>, <a href="https://arxiv.org/ps/1307.4333">ps</a>, <a href="https://arxiv.org/format/1307.4333">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1016/j.optcom.2014.07.029">10.1016/j.optcom.2014.07.029 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Building patterns by traveling vortices and dipoles in periodic dissipative media </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Besse%2C+V">Valentin Besse</a>, <a href="/search/?searchtype=author&query=Leblond%2C+H">Herve Leblond</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1307.4333v5-abstract-short" style="display: inline;"> We analyze pattern-formation scenarios in the two-dimensional (2D) complex Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a cellular potential. The equation models laser cavities with built-in gratings, which are used to stabilize 2D patterns. The pattern-building process is initiated by kicking a localized compound mode, in the form of a dipole, quadrupole, or vortex… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1307.4333v5-abstract-full').style.display = 'inline'; document.getElementById('1307.4333v5-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1307.4333v5-abstract-full" style="display: none;"> We analyze pattern-formation scenarios in the two-dimensional (2D) complex Ginzburg-Landau (CGL) equation with the cubic-quintic (CQ) nonlinearity and a cellular potential. The equation models laser cavities with built-in gratings, which are used to stabilize 2D patterns. The pattern-building process is initiated by kicking a localized compound mode, in the form of a dipole, quadrupole, or vortex which is composed of four local peaks. The hopping motion of the kicked mode through the cellular structure leads to the generation of various extended patterns pinned by the structure. In the ring-shaped system, the persisting freely moving dipole hits the stationary pattern from the opposite side, giving rise to several dynamical regimes, with the pinned multi-soliton chain playing the role of the Newton's cradle (NC). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1307.4333v5-abstract-full').style.display = 'none'; document.getElementById('1307.4333v5-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 June, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 July, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2013. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1307.1534">arXiv:1307.1534</a> <span> [<a href="https://arxiv.org/pdf/1307.1534">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> High power pulses extracted from the Peregrine rogue wave </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Yang%2C+G">Guangye Yang</a>, <a href="/search/?searchtype=author&query=Li%2C+L">Lu Li</a>, <a href="/search/?searchtype=author&query=Jia%2C+S">SuoTang Jia</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1307.1534v2-abstract-short" style="display: inline;"> We address the various initial excitations of the Peregrine rogue wave and establish a robust transmission scheme of high power pulses extracted from the Peregrine rogue wave in a standard telecommunications fiber. The results show that the Peregrine rogue wave can be excited by using a weak pulse atop a continuous wave background and that the high power pulses extracted from the Peregrine rogue w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1307.1534v2-abstract-full').style.display = 'inline'; document.getElementById('1307.1534v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1307.1534v2-abstract-full" style="display: none;"> We address the various initial excitations of the Peregrine rogue wave and establish a robust transmission scheme of high power pulses extracted from the Peregrine rogue wave in a standard telecommunications fiber. The results show that the Peregrine rogue wave can be excited by using a weak pulse atop a continuous wave background and that the high power pulses extracted from the Peregrine rogue wave exhibit the typical characteristics of breathing solitons. The influence of higher-order effects, such as the third-order dispersion, the self-steepening and the Raman effect, on the propagation of the pulse extracted from the peak position and the interaction between neighboring high power pulses induced by initial perturbations are also investigated. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1307.1534v2-abstract-full').style.display = 'none'; document.getElementById('1307.1534v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 September, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 July, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Rom. Rep. Phys. 65, 391 (2013) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1307.1533">arXiv:1307.1533</a> <span> [<a href="https://arxiv.org/pdf/1307.1533">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> Control of high power pulse extracted from the maximally compressed pulse in a nonlinear optical fiber </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Yang%2C+G">Guangye Yang</a>, <a href="/search/?searchtype=author&query=Li%2C+L">Lu Li</a>, <a href="/search/?searchtype=author&query=Jia%2C+S">Suotang Jia</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1307.1533v2-abstract-short" style="display: inline;"> We address the possibility to control high power pulses extracted from the maximally compressed pulse in a nonlinear optical fiber by adjusting the initial excitation parameters. The numerical results show that the power, location and splitting order number of the maximally compressed pulse and the transmission features of high power pulses extracted from the maximally compressed pulse can be mani… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1307.1533v2-abstract-full').style.display = 'inline'; document.getElementById('1307.1533v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1307.1533v2-abstract-full" style="display: none;"> We address the possibility to control high power pulses extracted from the maximally compressed pulse in a nonlinear optical fiber by adjusting the initial excitation parameters. The numerical results show that the power, location and splitting order number of the maximally compressed pulse and the transmission features of high power pulses extracted from the maximally compressed pulse can be manipulated through adjusting the modulation amplitude, width, and phase of the initial Gaussian-type perturbation pulse on a continuous wave background. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1307.1533v2-abstract-full').style.display = 'none'; document.getElementById('1307.1533v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 September, 2013; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 July, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 7 figures, The paper has been accepted by Rom. Rep. Phys</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1206.1900">arXiv:1206.1900</a> <span> [<a href="https://arxiv.org/pdf/1206.1900">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> </div> <p class="title is-5 mathjax"> Generations of polygonal soliton clusters and fundamental solitons by radially-azimuthally phase-modulated necklace-ring beams in dissipative systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=He%2C+Y">Yingji He</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a>, <a href="/search/?searchtype=author&query=Qiu%2C+Y">Yunli Qiu</a>, <a href="/search/?searchtype=author&query=Chen%2C+Z">Zhanxu Chen</a>, <a href="/search/?searchtype=author&query=Li%2C+Y">Yifang Li</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1206.1900v1-abstract-short" style="display: inline;"> We demonstrate that, in a two-dimensional dissipative medium described by the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) equation with the viscous (spectral-filtering) term, necklace rings carrying a mixed radial-azimuthal phase modulation can evolve into polygonal or quasi-polygonal stable soliton clusters, and into stable fundamental solitons. The outcome of the evolution is controlled by… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1206.1900v1-abstract-full').style.display = 'inline'; document.getElementById('1206.1900v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1206.1900v1-abstract-full" style="display: none;"> We demonstrate that, in a two-dimensional dissipative medium described by the cubic-quintic (CQ) complex Ginzburg-Landau (CGL) equation with the viscous (spectral-filtering) term, necklace rings carrying a mixed radial-azimuthal phase modulation can evolve into polygonal or quasi-polygonal stable soliton clusters, and into stable fundamental solitons. The outcome of the evolution is controlled by the depth and azimuthal anharmonicity of the phase-modulation profile, or by the radius and number of "beads" in the initial necklace ring. Threshold characteristics of the evolution of the patterns are identified and explained. Parameter regions for the formation of the stable polygonal and quasi-polygonal soliton clusters, and of stable fundamental solitons, are identified. The model with the CQ terms replaced by the full saturable nonlinearity produces essentially the same set of the basic dynamical scenarios; hence this set is a universal one for the CGL models. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1206.1900v1-abstract-full').style.display = 'none'; document.getElementById('1206.1900v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 June, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages, 8 figures, Physical Review E, in press</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1206.1497">arXiv:1206.1497</a> <span> [<a href="https://arxiv.org/pdf/1206.1497">pdf</a>, <a href="https://arxiv.org/ps/1206.1497">ps</a>, <a href="https://arxiv.org/format/1206.1497">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevE.87.012916">10.1103/PhysRevE.87.012916 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Pattern formation by kicked solitons in the two-dimensionnal Ginzburg-Landau medium with a transverse grating </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Besse%2C+V">Valentin Besse</a>, <a href="/search/?searchtype=author&query=Leblond%2C+H">Herv茅 Leblond</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">Boris A. Malomed</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1206.1497v3-abstract-short" style="display: inline;"> We consider the kick-induced mobility of two-dimensional (2D) fundamental dissipative solitons in models of lasing media based on the 2D complex Ginzburg-Landau (CGL) equation including a spatially periodic potential (transverse grating). The depinning threshold is identified by means of systematic simulations, and described by means of an analytical approximation, depending on the orientation of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1206.1497v3-abstract-full').style.display = 'inline'; document.getElementById('1206.1497v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1206.1497v3-abstract-full" style="display: none;"> We consider the kick-induced mobility of two-dimensional (2D) fundamental dissipative solitons in models of lasing media based on the 2D complex Ginzburg-Landau (CGL) equation including a spatially periodic potential (transverse grating). The depinning threshold is identified by means of systematic simulations, and described by means of an analytical approximation, depending on the orientation of the kick. Various pattern-formation scenarios are found above the threshold. Most typically, the soliton, hopping between potential cells, leaves arrayed patterns of different sizes in its wake. In the laser cavity, this effect may be used as a mechanism for selective pattern formation controlled by the tilt of the seed beam. Freely moving solitons feature two distinct values of the established velocity. Elastic and inelastic collisions between free solitons and pinned arrayed patterns are studied too. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1206.1497v3-abstract-full').style.display = 'none'; document.getElementById('1206.1497v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 December, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 June, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 20 figures (with 41 sub-figures)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1204.4772">arXiv:1204.4772</a> <span> [<a href="https://arxiv.org/pdf/1204.4772">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1364/OL.37.002526">10.1364/OL.37.002526 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Stable surface solitons in truncated complex potentials </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=He%2C+Y">Yingji He</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a>, <a href="/search/?searchtype=author&query=Zhu%2C+X">Xing Zhu</a>, <a href="/search/?searchtype=author&query=Guo%2C+L">Lina Guo</a>, <a href="/search/?searchtype=author&query=Kartashov%2C+Y+V">Yaroslav V. Kartashov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1204.4772v1-abstract-short" style="display: inline;"> We show that surface solitons in the one-dimensional nonlinear Schr枚dinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interv… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.4772v1-abstract-full').style.display = 'inline'; document.getElementById('1204.4772v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1204.4772v1-abstract-full" style="display: none;"> We show that surface solitons in the one-dimensional nonlinear Schr枚dinger equation with truncated complex periodic potential can be stabilized by linear homogeneous losses, which are necessary to balance gain in the near-surface channel arising from the imaginary part of potential. Such solitons become stable attractors when the strength of homogeneous losses acquires values from a limited interval and they exist in focusing and defocusing media. The domains of stability of surface solitons shrink with increase of the amplitude of imaginary part of complex potential. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1204.4772v1-abstract-full').style.display = 'none'; document.getElementById('1204.4772v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 April, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">3 pages, 4 figures,accepted by Optics Letters</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1105.5769">arXiv:1105.5769</a> <span> [<a href="https://arxiv.org/pdf/1105.5769">pdf</a>, <a href="https://arxiv.org/format/1105.5769">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.83.063825">10.1103/PhysRevA.83.063825 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spatiotemporal vortex solitons in hexagonal arrays of waveguides </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Leblond%2C+H">H. Leblond</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">B. A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">D. Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1105.5769v1-abstract-short" style="display: inline;"> By means of a systematic numerical analysis, we demonstrate that hexagonal lattices of parallel linearly-coupled waveguides, with the intrinsic cubic self-focusing nonlinearity, give rise to three species of stable semi-discrete complexes (which are continuous in the longitudinal direction), with embedded vorticity S: triangular modes with S=1, hexagonal ones with S=2, both centered around an empt… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1105.5769v1-abstract-full').style.display = 'inline'; document.getElementById('1105.5769v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1105.5769v1-abstract-full" style="display: none;"> By means of a systematic numerical analysis, we demonstrate that hexagonal lattices of parallel linearly-coupled waveguides, with the intrinsic cubic self-focusing nonlinearity, give rise to three species of stable semi-discrete complexes (which are continuous in the longitudinal direction), with embedded vorticity S: triangular modes with S=1, hexagonal ones with S=2, both centered around an empty central core, and compact triangles with S=1, which do not not include the empty site. Collisions between stable triangular vortices are studied too. These waveguiding lattices can be realized in optics and BEC. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1105.5769v1-abstract-full').style.display = 'none'; document.getElementById('1105.5769v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 May, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 14 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1104.2053">arXiv:1104.2053</a> <span> [<a href="https://arxiv.org/pdf/1104.2053">pdf</a>, <a href="https://arxiv.org/ps/1104.2053">ps</a>, <a href="https://arxiv.org/format/1104.2053">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PHYSREVA.80.053812">10.1103/PHYSREVA.80.053812 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Ultrashort spatiotemporal optical solitons in quadratic nonlinear media: Generation of line and lump solitons from few-cycle input pulses </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Leblond%2C+H">Herv茅 Leblond</a>, <a href="/search/?searchtype=author&query=Kremer%2C+D">David Kremer</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1104.2053v1-abstract-short" style="display: inline;"> By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of bo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1104.2053v1-abstract-full').style.display = 'inline'; document.getElementById('1104.2053v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1104.2053v1-abstract-full" style="display: none;"> By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of the perturbed unstable line soliton into stable lumps for a quadratic nonlinear medium with anomalous dispersion is also given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1104.2053v1-abstract-full').style.display = 'none'; document.getElementById('1104.2053v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 April, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review A 80 (2009) 53812 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1102.1285">arXiv:1102.1285</a> <span> [<a href="https://arxiv.org/pdf/1102.1285">pdf</a>, <a href="https://arxiv.org/ps/1102.1285">ps</a>, <a href="https://arxiv.org/format/1102.1285">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PHYSREVA.81.033824">10.1103/PHYSREVA.81.033824 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Collapse of ultrashort spatiotemporal pulses described by the cubic generalized Kadomtsev-Petviashvili equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Leblond%2C+H">Herv茅 Leblond</a>, <a href="/search/?searchtype=author&query=Kremer%2C+D">David Kremer</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1102.1285v1-abstract-short" style="display: inline;"> By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.1285v1-abstract-full').style.display = 'inline'; document.getElementById('1102.1285v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1102.1285v1-abstract-full" style="display: none;"> By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated over the transverse spatial coordinate) is given and a strongly asymmetric spectral broadening of ultrashort spatiotemporal pulses during collapse is evidenced. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.1285v1-abstract-full').style.display = 'none'; document.getElementById('1102.1285v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 February, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review A 81 (2010) 33824 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1102.1284">arXiv:1102.1284</a> <span> [<a href="https://arxiv.org/pdf/1102.1284">pdf</a>, <a href="https://arxiv.org/ps/1102.1284">ps</a>, <a href="https://arxiv.org/format/1102.1284">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PHYSREVA.81.063815">10.1103/PHYSREVA.81.063815 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Ultrashort light bullets described by the two-dimensional sine-Gordon equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Leblond%2C+H">Herv茅 Leblond</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">Dumitru Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1102.1284v1-abstract-short" style="display: inline;"> By using a reductive perturbation technique applied to a two-level model, this study puts forward a generic two-dimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly varying envelope approximation. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.1284v1-abstract-full').style.display = 'inline'; document.getElementById('1102.1284v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1102.1284v1-abstract-full" style="display: none;"> By using a reductive perturbation technique applied to a two-level model, this study puts forward a generic two-dimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly varying envelope approximation. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and that robust (2+1)-dimensional ultrashort light bullets may form from adequately chosen few-cycle input spatiotemporal wave forms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time and are therefore not steady-state lumps. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1102.1284v1-abstract-full').style.display = 'none'; document.getElementById('1102.1284v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 February, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Physical Review A 81 (2010) 63815 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1012.3567">arXiv:1012.3567</a> <span> [<a href="https://arxiv.org/pdf/1012.3567">pdf</a>, <a href="https://arxiv.org/ps/1012.3567">ps</a>, <a href="https://arxiv.org/format/1012.3567">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Pattern Formation and Solitons">nlin.PS</span> </div> </div> <p class="title is-5 mathjax"> Two-dimensional subwavelength plasmonic lattice solitons </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Ye%2C+F">F. Ye</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">D. Mihalache</a>, <a href="/search/?searchtype=author&query=Hu%2C+B">B. Hu</a>, <a href="/search/?searchtype=author&query=Panoiu%2C+N+C">N. C. Panoiu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1012.3567v2-abstract-short" style="display: inline;"> We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detail. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1012.3567v2-abstract-full" style="display: none;"> We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detail. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1012.3567v2-abstract-full').style.display = 'none'; document.getElementById('1012.3567v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 December, 2010; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 December, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 4 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1008.0224">arXiv:1008.0224</a> <span> [<a href="https://arxiv.org/pdf/1008.0224">pdf</a>, <a href="https://arxiv.org/ps/1008.0224">ps</a>, <a href="https://arxiv.org/format/1008.0224">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevA.82.023813">10.1103/PhysRevA.82.023813 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Stable topological modes in two-dimensional Ginzburg-Landau models with trapping potentials </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Mihalache%2C+D">D. Mihalache</a>, <a href="/search/?searchtype=author&query=Mazilu%2C+D">D. Mazilu</a>, <a href="/search/?searchtype=author&query=Skarka%2C+V">V. Skarka</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">B. A. Malomed</a>, <a href="/search/?searchtype=author&query=Leblond%2C+H">H. Leblond</a>, <a href="/search/?searchtype=author&query=Aleksi%C4%87%2C+N+B">N. B. Aleksi膰</a>, <a href="/search/?searchtype=author&query=Lederer%2C+F">F. Lederer</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1008.0224v1-abstract-short" style="display: inline;"> Complex Ginzburg-Landau (CGL) models of laser media (with the cubic-quintic nonlinearity) do not contain an effective diffusion term, which makes all vortex solitons unstable in these models. Recently, it has been demonstrated that the addition of a two-dimensional periodic potential, which may be induced by a transverse grating in the laser cavity, to the CGL equation stabilizes compound (four-pe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1008.0224v1-abstract-full').style.display = 'inline'; document.getElementById('1008.0224v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1008.0224v1-abstract-full" style="display: none;"> Complex Ginzburg-Landau (CGL) models of laser media (with the cubic-quintic nonlinearity) do not contain an effective diffusion term, which makes all vortex solitons unstable in these models. Recently, it has been demonstrated that the addition of a two-dimensional periodic potential, which may be induced by a transverse grating in the laser cavity, to the CGL equation stabilizes compound (four-peak) vortices, but the most fundamental "crater-shaped" vortices (CSVs), alias vortex rings, which are, essentially, squeezed into a single cell of the potential, have not been found before in a stable form. In this work we report families of stable compact CSVs with vorticity S=1 in the CGL model with the external potential of two different types: an axisymmetric parabolic trap, and the periodic potential. In both cases, we identify stability region for the CSVs and for the fundamental solitons (S=0). Those CSVs which are unstable in the axisymmetric potential break up into robust dipoles. All the vortices with S=2 are unstable, splitting into tripoles. Stability regions for the dipoles and tripoles are identified too. The periodic potential cannot stabilize CSVs with S>=2 either; instead, families of stable compact square-shaped quadrupoles are found. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1008.0224v1-abstract-full').style.display = 'none'; document.getElementById('1008.0224v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 August, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2010. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1007.3030">arXiv:1007.3030</a> <span> [<a href="https://arxiv.org/pdf/1007.3030">pdf</a>, <a href="https://arxiv.org/ps/1007.3030">ps</a>, <a href="https://arxiv.org/format/1007.3030">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Optics">physics.optics</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.105.213901">10.1103/PhysRevLett.105.213901 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The variety of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Skarka%2C+V">V. Skarka</a>, <a href="/search/?searchtype=author&query=Aleksi%C4%87%2C+N+B">N. B. Aleksi膰</a>, <a href="/search/?searchtype=author&query=Leblond%2C+H">H. Leblond</a>, <a href="/search/?searchtype=author&query=Malomed%2C+B+A">B. A. Malomed</a>, <a href="/search/?searchtype=author&query=Mihalache%2C+D">D. Mihalache</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1007.3030v1-abstract-short" style="display: inline;"> Using a combination of the variation approximation (VA) and direct simulations, we consider the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous los… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1007.3030v1-abstract-full').style.display = 'inline'; document.getElementById('1007.3030v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1007.3030v1-abstract-full" style="display: none;"> Using a combination of the variation approximation (VA) and direct simulations, we consider the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provide for the hitherto elusive stabilization of vortex solitons in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, including spinning elliptically shaped ones, eccentric elliptic vortices which feature double rotation, spinning crescents, and breathing vortices. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1007.3030v1-abstract-full').style.display = 'none'; document.getElementById('1007.3030v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 July, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2010. </p> </li> </ol> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Mihalache%2C+D&start=50" class="pagination-next" >Next </a> <ul 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