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wave solutions</title> <meta name="description" content="Search results for: solitary wave solutions"> <meta name="keywords" content="solitary wave solutions"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="solitary wave solutions"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 5258</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: solitary wave solutions</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5258</span> Symbolic Computation and Abundant Travelling Wave Solutions to Modified Burgers' Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Younis">Muhammad Younis</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, the novel (G′/G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the modified Burgers’ equation with the aid of computation. The method is reliable and useful, which gives more general exact travelling wave solutions than the existing methods. These obtained solutions are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Some of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=traveling%20wave%20solutions" title="traveling wave solutions">traveling wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=NLPDE" title=" NLPDE"> NLPDE</a>, <a href="https://publications.waset.org/abstracts/search?q=computation" title=" computation"> computation</a>, <a href="https://publications.waset.org/abstracts/search?q=integrability" title=" integrability"> integrability</a> </p> <a href="https://publications.waset.org/abstracts/48762/symbolic-computation-and-abundant-travelling-wave-solutions-to-modified-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48762.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">433</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5257</span> Mapping Methods to Solve a Modified Korteweg de Vries Type Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=E.%20V.%20Krishnan">E. V. Krishnan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=travelling%20wave%20solutions" title="travelling wave solutions">travelling wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=Jacobi%20elliptic%20functions" title=" Jacobi elliptic functions"> Jacobi elliptic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20wave%20solutions" title=" solitary wave solutions"> solitary wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=Korteweg-de%20Vries%20equation" title=" Korteweg-de Vries equation"> Korteweg-de Vries equation</a> </p> <a href="https://publications.waset.org/abstracts/12150/mapping-methods-to-solve-a-modified-korteweg-de-vries-type-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12150.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">331</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5256</span> Second Order Solitary Solutions to the Hodgkin-Huxley Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tadas%20Telksnys">Tadas Telksnys</a>, <a href="https://publications.waset.org/abstracts/search?q=Zenonas%20Navickas"> Zenonas Navickas</a>, <a href="https://publications.waset.org/abstracts/search?q=Minvydas%20Ragulskis"> Minvydas Ragulskis</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Necessary and sufficient conditions for the existence of second order solitary solutions to the Hodgkin-Huxley equation are derived in this paper. The generalized multiplicative operator of differentiation helps not only to construct closed-form solitary solutions but also automatically generates conditions of their existence in the space of the equation's parameters and initial conditions. It is demonstrated that bright, kink-type solitons and solitary solutions with singularities can exist in the Hodgkin-Huxley equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hodgkin-Huxley%20equation" title="Hodgkin-Huxley equation">Hodgkin-Huxley equation</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20solution" title=" solitary solution"> solitary solution</a>, <a href="https://publications.waset.org/abstracts/search?q=existence%20condition" title=" existence condition"> existence condition</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20method" title=" operator method"> operator method</a> </p> <a href="https://publications.waset.org/abstracts/37370/second-order-solitary-solutions-to-the-hodgkin-huxley-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37370.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">381</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5255</span> Exact Solutions of K(N,N)-Type Equations Using Jacobi Elliptic Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Edamana%20Krishnan">Edamana Krishnan</a>, <a href="https://publications.waset.org/abstracts/search?q=Khalil%20Al-Ghafri"> Khalil Al-Ghafri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=travelling%20wave%20solutions" title="travelling wave solutions">travelling wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20wave%20solutions" title=" solitary wave solutions"> solitary wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=compactons" title=" compactons"> compactons</a>, <a href="https://publications.waset.org/abstracts/search?q=Jacobi%20elliptic%20functions" title=" Jacobi elliptic functions"> Jacobi elliptic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=mapping%20methods" title=" mapping methods"> mapping methods</a> </p> <a href="https://publications.waset.org/abstracts/59011/exact-solutions-of-knn-type-equations-using-jacobi-elliptic-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59011.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">305</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5254</span> Sensitivity Analysis and Solitary Wave Solutions to the (2+1)-Dimensional Boussinesq Equation in Dispersive Media</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Naila%20Nasreen">Naila Nasreen</a>, <a href="https://publications.waset.org/abstracts/search?q=Dianchen%20Lu"> Dianchen Lu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%282%2B1%29-dimensional%20Boussinesq%20equation" title="(2+1)-dimensional Boussinesq equation">(2+1)-dimensional Boussinesq equation</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20wave%20solutions" title=" solitary wave solutions"> solitary wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=Ricatti%20equation%20mapping%20approach" title=" Ricatti equation mapping approach"> Ricatti equation mapping approach</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20phenomena" title=" nonlinear phenomena"> nonlinear phenomena</a> </p> <a href="https://publications.waset.org/abstracts/165781/sensitivity-analysis-and-solitary-wave-solutions-to-the-21-dimensional-boussinesq-equation-in-dispersive-media" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165781.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">100</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5253</span> Nonlinear Modelling of Sloshing Waves and Solitary Waves in Shallow Basins</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20R.%20Jalali">Mohammad R. Jalali</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20M.%20Jalali"> Mohammad M. Jalali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, <em>x-</em>direction and <em>y-</em>direction. The effect of vertical direction (<em>z-</em>direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the <em>x</em>-axis and the interaction of solitary waves with each other are conducted to validate the developed model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Green%E2%80%93Naghdi%20equations" title="Green–Naghdi equations">Green–Naghdi equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinearity" title=" nonlinearity"> nonlinearity</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20prediction" title=" numerical prediction"> numerical prediction</a>, <a href="https://publications.waset.org/abstracts/search?q=sloshing%20waves" title=" sloshing waves"> sloshing waves</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20waves" title=" solitary waves"> solitary waves</a> </p> <a href="https://publications.waset.org/abstracts/86905/nonlinear-modelling-of-sloshing-waves-and-solitary-waves-in-shallow-basins" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86905.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">285</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5252</span> Symbolic Computation for the Multi-Soliton Solutions of a Class of Fifth-Order Evolution Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rafat%20Alshorman">Rafat Alshorman</a>, <a href="https://publications.waset.org/abstracts/search?q=Fadi%20Awawdeh"> Fadi Awawdeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multiple%20soliton%20solutions" title="multiple soliton solutions">multiple soliton solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=fifth-order%20evolution%20equations" title=" fifth-order evolution equations"> fifth-order evolution equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Cole-Hopf%20transformation" title=" Cole-Hopf transformation"> Cole-Hopf transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=Hirota%20bilinear%20method" title=" Hirota bilinear method"> Hirota bilinear method</a> </p> <a href="https://publications.waset.org/abstracts/9376/symbolic-computation-for-the-multi-soliton-solutions-of-a-class-of-fifth-order-evolution-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9376.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">319</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5251</span> Spherical Nonlinear Wave Propagation in Relativistic Quantum Plasma</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alireza%20Abdikian">Alireza Abdikian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> By assuming a quantum relativistic degenerate electron-positron (e-p) plasma media, the nonlinear acoustic solitary propagation in the presence of the stationary ions for neutralizing the plasma background of bounded cylindrical geometry was investigated. By using the standard reductive perturbation technique with cooperation the quantum hydrodynamics model for the e-p fluid, the spherical Kadomtsev-Petviashvili equation was derived for small but finite amplitude waves and was given the solitary wave solution for the parameters relevant for dense astrophysical objects such as white dwarf stars. By using a suitable coordinate transformation and using improved F-expansion technique, the SKP equation can be solved analytically. The numerical results reveal that the relativistic effects lead to propagate the electrostatic bell shape structures and by increasing the relativistic effects, the amplitude and the width of the e-p acoustic solitary wave will decrease. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Electron-positron%20plasma" title="Electron-positron plasma">Electron-positron plasma</a>, <a href="https://publications.waset.org/abstracts/search?q=Acoustic%20solitary%20wave" title=" Acoustic solitary wave"> Acoustic solitary wave</a>, <a href="https://publications.waset.org/abstracts/search?q=Relativistic%20plasmas" title=" Relativistic plasmas"> Relativistic plasmas</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20spherical%20Kadomtsev-Petviashvili%20equation" title=" the spherical Kadomtsev-Petviashvili equation"> the spherical Kadomtsev-Petviashvili equation</a> </p> <a href="https://publications.waset.org/abstracts/125010/spherical-nonlinear-wave-propagation-in-relativistic-quantum-plasma" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125010.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">142</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5250</span> Propagation of W Shaped of Solitons in Fiber Bragg Gratings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mezghiche%20Kamel">Mezghiche Kamel</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the ﬁber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%EF%AC%81ber%20bragg%20grating" title="ﬁber bragg grating">ﬁber bragg grating</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear-coupled%20mode%20equations" title=" nonlinear-coupled mode equations"> nonlinear-coupled mode equations</a>, <a href="https://publications.waset.org/abstracts/search?q=w%20shaped%20of%20solitons" title=" w shaped of solitons"> w shaped of solitons</a>, <a href="https://publications.waset.org/abstracts/search?q=PNLS" title=" PNLS"> PNLS</a> </p> <a href="https://publications.waset.org/abstracts/12669/propagation-of-w-shaped-of-solitons-in-fiber-bragg-gratings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12669.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">769</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5249</span> Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tsun-Hui%20Huang">Tsun-Hui Huang</a>, <a href="https://publications.waset.org/abstracts/search?q=Shyue-Cheng%20Yang"> Shyue-Cheng Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Chiou-Fen%20Shieha"> Chiou-Fen Shieha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=polynomial%20constitutive%20equation" title="polynomial constitutive equation">polynomial constitutive equation</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary" title=" solitary"> solitary</a>, <a href="https://publications.waset.org/abstracts/search?q=stress%20solitary%20waves" title=" stress solitary waves"> stress solitary waves</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20constitutive%20law" title=" nonlinear constitutive law"> nonlinear constitutive law</a> </p> <a href="https://publications.waset.org/abstracts/10185/stress-solitary-waves-generated-by-a-second-order-polynomial-constitutive-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10185.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">497</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5248</span> Soliton Solutions of the Higher-Order Nonlinear Schrödinger Equation with Dispersion Effects</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Triki">H. Triki</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Hamaizi"> Y. Hamaizi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20El-Akrmi"> A. El-Akrmi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Schr%C3%B6dinger%20equation" title="nonlinear Schrödinger equation">nonlinear Schrödinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=high-order%20effects" title=" high-order effects"> high-order effects</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20solution" title=" soliton solution"> soliton solution</a> </p> <a href="https://publications.waset.org/abstracts/11564/soliton-solutions-of-the-higher-order-nonlinear-schrodinger-equation-with-dispersion-effects" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11564.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">635</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5247</span> Exactly Fractional Solutions of Nonlinear Lattice Equation via Some Fractional Transformations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Zerarka">A. Zerarka</a>, <a href="https://publications.waset.org/abstracts/search?q=W.%20Djoudi"> W. Djoudi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20transformations" title="fractional transformations">fractional transformations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20equation" title=" nonlinear equation"> nonlinear equation</a>, <a href="https://publications.waset.org/abstracts/search?q=travelling%20wave%20solutions" title=" travelling wave solutions"> travelling wave solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=lattice%20equation" title=" lattice equation "> lattice equation </a> </p> <a href="https://publications.waset.org/abstracts/20487/exactly-fractional-solutions-of-nonlinear-lattice-equation-via-some-fractional-transformations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20487.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">657</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5246</span> Who Killed Kalief? Examining the Effects of Solitary Confinement on Juvenile Detainees in the United States</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Esther%20Baldwin">Esther Baldwin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is well settled that the use of solitary confinement can cause psychological and physical harm to detainees. For juveniles, who are more susceptible to irreparable harm due to their underdeveloped psyches, the risks are exacerbated. Despite these risks, across the United States juvenile detainees are regularly held in isolation for prolonged periods of time. This essay will examine the broad impact of solitary confinement on juvenile detainees while giving particular focus to the story of Kalief Browder, a juvenile awaiting trial on Rikers Island in New York for a period of three years, nearly two years of which were spent in solitary confinement. Although sadly, his story is not uncommon, Kalief’s story offers a unique perspective in that it provides first-hand insight on the effects of solitary confinement on juveniles. It is our hope that by sharing his story, we will demand better detention practices and policies for juveniles under correctional control in the United States. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=criminal%20justice%20system" title="criminal justice system">criminal justice system</a>, <a href="https://publications.waset.org/abstracts/search?q=juveniles" title=" juveniles"> juveniles</a>, <a href="https://publications.waset.org/abstracts/search?q=Kalief%20browder" title=" Kalief browder"> Kalief browder</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20confinement" title=" solitary confinement"> solitary confinement</a> </p> <a href="https://publications.waset.org/abstracts/46258/who-killed-kalief-examining-the-effects-of-solitary-confinement-on-juvenile-detainees-in-the-united-states" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46258.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">322</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5245</span> Nonlinear Internal Waves in Rotating Ocean</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=L.%20A.%20Ostrovsky">L. A. Ostrovsky</a>, <a href="https://publications.waset.org/abstracts/search?q=Yu.%20A.%20Stepanyants"> Yu. A. Stepanyants</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Earth%20rotation" title="Earth rotation">Earth rotation</a>, <a href="https://publications.waset.org/abstracts/search?q=internal%20waves" title=" internal waves"> internal waves</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20waves" title=" nonlinear waves"> nonlinear waves</a>, <a href="https://publications.waset.org/abstracts/search?q=solitons" title=" solitons"> solitons</a> </p> <a href="https://publications.waset.org/abstracts/28004/nonlinear-internal-waves-in-rotating-ocean" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28004.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">672</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5244</span> Modeling of Long Wave Generation and Propagation via Seabed Deformation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chih-Hua%20Chang">Chih-Hua Chang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study uses a three-dimensional (3D) fully nonlinear model to simulate the wave generation problem caused by the movement of the seabed. The numerical model is first simplified into two dimensions and then compared with the existing two-dimensional (2D) experimental data and the 2D numerical results of other shallow-water wave models. Results show that this model is different from the earlier shallow-water wave models, with the phase being closer to the experimental results of wave propagation. The results of this study are also compared with those of the 3D experimental results of other researchers. Satisfactory results can be obtained in both the waveform and the flow field. This study assesses the application of the model to simulate the wave caused by the circular (radius r0) terrain rising or falling (moving distance bm). The influence of wave-making parameters r0 and bm are discussed. This study determines that small-range (e.g., r0 = 2, normalized by the static water depth), rising, or sinking terrain will produce significant wave groups in the far field. For large-scale moving terrain (e.g., r0 = 10), uplift and deformation will potentially generate the leading solitary-like waves in the far field. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=seismic%20wave" title="seismic wave">seismic wave</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20generation" title=" wave generation"> wave generation</a>, <a href="https://publications.waset.org/abstracts/search?q=far-field%20waves" title=" far-field waves"> far-field waves</a>, <a href="https://publications.waset.org/abstracts/search?q=seabed%20deformation" title=" seabed deformation"> seabed deformation</a> </p> <a href="https://publications.waset.org/abstracts/158851/modeling-of-long-wave-generation-and-propagation-via-seabed-deformation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/158851.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">86</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5243</span> Comparative Study of Soliton Collisions in Uniform and Nonuniform Magnetized Plasma</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Renu%20Tomar">Renu Tomar</a>, <a href="https://publications.waset.org/abstracts/search?q=Hitendra%20K.%20Malik"> Hitendra K. Malik</a>, <a href="https://publications.waset.org/abstracts/search?q=Raj%20P.%20Dahiya"> Raj P. Dahiya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Similar to the sound waves in air, plasmas support the propagation of ion waves, which evolve into the solitary structures when the effect of non linearity and dispersion are balanced. The ion acoustic solitary waves have been investigated in details in homogeneous plasmas, inhomogeneous plasmas, and magnetized plasmas. The ion acoustic solitary waves are also found to reflect from a density gradient or boundary present in the plasma after propagating. Another interesting feature of the solitary waves is their collision. In the present work, we carry out analytical calculations for the head-on collision of solitary waves in a magnetized plasma which has dust grains in addition to the ions and electrons. For this, we employ Poincar´e-Lighthill-Kuo (PLK) method. To lowest nonlinear order, the problem of colliding solitary waves leads to KdV (modified KdV) equations and also yields the phase shifts that occur in the interaction. These calculations are accomplished for the uniform and nonuniform plasmas, and the results on the soliton properties are discussed in detail. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inhomogeneous%20magnetized%20plasma" title="inhomogeneous magnetized plasma">inhomogeneous magnetized plasma</a>, <a href="https://publications.waset.org/abstracts/search?q=dust%20charging" title=" dust charging"> dust charging</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20collisions" title=" soliton collisions"> soliton collisions</a>, <a href="https://publications.waset.org/abstracts/search?q=magnetized%20plasma" title=" magnetized plasma"> magnetized plasma</a> </p> <a href="https://publications.waset.org/abstracts/14740/comparative-study-of-soliton-collisions-in-uniform-and-nonuniform-magnetized-plasma" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14740.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">470</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5242</span> Gall Bladder Polyp Identified as Solitary RCC Metastasis 4 Years after Nephrectomy: An Unusual Case Report</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gerard%20Bray">Gerard Bray</a>, <a href="https://publications.waset.org/abstracts/search?q=Arya%20Bahadori"> Arya Bahadori</a>, <a href="https://publications.waset.org/abstracts/search?q=Sachinka%20Ranasinghe"> Sachinka Ranasinghe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Renal cell carcinoma (RCC) is among the top 10 most common cancers worldwide, where metastatic disease carries a poor prognosis. Herein, we present a 74-year-old male presenting with asymptomatic solitary metachronous metastasis to the gall bladder 4 years following nephrectomy for clear cell RCC. Solitary RCC metastasis to the gall bladder following nephrectomy is rarely reported in the literature and brings with it a clinical conundrum of whether surgical resection or systemic therapy should be utilized. In this case, surgical excision with cholecystectomy was employed without systemic therapy. We, therefore, contribute a rare and interesting case that highlights that metastasectomy of a solitary metastasis can improve survival according to current literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=renal%20cell%20carcinoma" title="renal cell carcinoma">renal cell carcinoma</a>, <a href="https://publications.waset.org/abstracts/search?q=gall%20bladder%20metastasis" title=" gall bladder metastasis"> gall bladder metastasis</a>, <a href="https://publications.waset.org/abstracts/search?q=solitary%20metastasectomy" title=" solitary metastasectomy"> solitary metastasectomy</a>, <a href="https://publications.waset.org/abstracts/search?q=metachronous" title=" metachronous"> metachronous</a> </p> <a href="https://publications.waset.org/abstracts/145137/gall-bladder-polyp-identified-as-solitary-rcc-metastasis-4-years-after-nephrectomy-an-unusual-case-report" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/145137.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">172</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5241</span> Soliton Solutions in (3+1)-Dimensions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Magdy%20G.%20Asaad">Magdy G. Asaad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Solitons are among the most beneficial solutions for science and technology for their applicability in physical applications including plasma, energy transport along protein molecules, wave transport along poly-acetylene molecules, ocean waves, constructing optical communication systems, transmission of information through optical fibers and Josephson junctions. In this talk, we will apply the bilinear technique to generate a class of soliton solutions to the (3+1)-dimensional nonlinear soliton equation of Jimbo-Miwa type. Examples of the resulting soliton solutions are computed and a few solutions are plotted. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pfaffian%20solutions" title="Pfaffian solutions">Pfaffian solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=N-soliton%20solutions" title=" N-soliton solutions"> N-soliton solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20equations" title=" soliton equations"> soliton equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Jimbo-Miwa" title=" Jimbo-Miwa"> Jimbo-Miwa</a> </p> <a href="https://publications.waset.org/abstracts/13463/soliton-solutions-in-31-dimensions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/13463.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">453</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5240</span> Gravitational Wave Solutions in Modified Gravity Theories</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hafiza%20Rizwana%20Kausar">Hafiza Rizwana Kausar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we formulate the wave equation in modified theories, particularly in f(R) theory, scalar-tensor theory, and metric palatine f(X) theory. We solve the wave equation in each case and try to find maximum possible solutions in the form polarization modes. It is found that modified theories present at most six modes however the mentioned metric theories allow four polarization modes, two of which are tensor in nature and other two are scalars. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=gravitational%20waves" title="gravitational waves">gravitational waves</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20theories" title=" modified theories"> modified theories</a>, <a href="https://publications.waset.org/abstracts/search?q=polariozation%20modes" title=" polariozation modes"> polariozation modes</a>, <a href="https://publications.waset.org/abstracts/search?q=scalar%20tensor%20theories" title=" scalar tensor theories"> scalar tensor theories</a> </p> <a href="https://publications.waset.org/abstracts/65098/gravitational-wave-solutions-in-modified-gravity-theories" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65098.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">363</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5239</span> Rogue Waves Arising on the Standing Periodic Wave in the High-Order Ablowitz-Ladik Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yanpei%20Zhen">Yanpei Zhen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The nonlinear Schrödinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable, and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves are generated on the periodic background. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Darboux%20transformation" title="Darboux transformation">Darboux transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=periodic%20wave" title=" periodic wave"> periodic wave</a>, <a href="https://publications.waset.org/abstracts/search?q=Rogue%20wave" title=" Rogue wave"> Rogue wave</a>, <a href="https://publications.waset.org/abstracts/search?q=separating%20the%20variables" title=" separating the variables"> separating the variables</a> </p> <a href="https://publications.waset.org/abstracts/174512/rogue-waves-arising-on-the-standing-periodic-wave-in-the-high-order-ablowitz-ladik-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/174512.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">183</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5238</span> Effect of Rotation on Love Wave Propagation in Piezoelectric Medium with Corrugation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Soniya%20Chaudhary">Soniya Chaudhary</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The present study analyses the propagation of Love wave in rotating piezoelectric layer lying over an elastic substrate with corrugated boundaries. The appropriate solutions in the considered medium satisfy the required boundary conditions to obtain the dispersion relation of Love wave for charge free as well as electrically shorted cases. The effects of rotation are shown by graphically on the non-dimensional speed of the Love wave. In addition to classical case, some existing results have been deduced as particular case of the present study. The present study may be useful in rotation sensor and SAW devices. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=corrugation" title="corrugation">corrugation</a>, <a href="https://publications.waset.org/abstracts/search?q=dispersion%20relation" title=" dispersion relation"> dispersion relation</a>, <a href="https://publications.waset.org/abstracts/search?q=love%20wave" title=" love wave"> love wave</a>, <a href="https://publications.waset.org/abstracts/search?q=piezoelectric" title=" piezoelectric"> piezoelectric</a> </p> <a href="https://publications.waset.org/abstracts/58153/effect-of-rotation-on-love-wave-propagation-in-piezoelectric-medium-with-corrugation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58153.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">225</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5237</span> Exact Solutions of a Nonlinear Schrodinger Equation with Kerr Law Nonlinearity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muna%20Alghabshi">Muna Alghabshi</a>, <a href="https://publications.waset.org/abstracts/search?q=Edmana%20Krishnan"> Edmana Krishnan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A nonlinear Schrodinger equation has been considered for solving by mapping methods in terms of Jacobi elliptic functions (JEFs). The equation under consideration has a linear evolution term, linear and nonlinear dispersion terms, the Kerr law nonlinearity term and three terms representing the contribution of meta materials. This equation which has applications in optical fibers is found to have soliton solutions, shock wave solutions, and singular wave solutions when the modulus of the JEFs approach 1 which is the infinite period limit. The equation with special values of the parameters has also been solved using the tanh method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jacobi%20elliptic%20function" title="Jacobi elliptic function">Jacobi elliptic function</a>, <a href="https://publications.waset.org/abstracts/search?q=mapping%20methods" title=" mapping methods"> mapping methods</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Schrodinger%20Equation" title=" nonlinear Schrodinger Equation"> nonlinear Schrodinger Equation</a>, <a href="https://publications.waset.org/abstracts/search?q=tanh%20method" title=" tanh method"> tanh method</a> </p> <a href="https://publications.waset.org/abstracts/55053/exact-solutions-of-a-nonlinear-schrodinger-equation-with-kerr-law-nonlinearity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55053.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">314</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5236</span> Nonlinear Propagation of Acoustic Soliton Waves in Dense Quantum Electron-Positron Magnetoplasma</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Abdikian">A. Abdikian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Propagation of nonlinear acoustic wave in dense electron-positron (e-p) plasmas in the presence of an external magnetic field and stationary ions (to neutralize the plasma background) is studied. By means of the quantum hydrodynamics model and applying the reductive perturbation method, the Zakharov-Kuznetsov equation is derived. Using the bifurcation theory of planar dynamical systems, the compressive structure of electrostatic solitary wave and periodic travelling waves is found. The numerical results show how the ion density ratio, the ion cyclotron frequency, and the direction cosines of the wave vector affect the nonlinear electrostatic travelling waves. The obtained results may be useful to better understand the obliquely nonlinear electrostatic travelling wave of small amplitude localized structures in dense magnetized quantum e-p plasmas and may be applicable to study the particle and energy transport mechanism in compact stars such as the interior of massive white dwarfs etc. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bifurcation%20theory" title="bifurcation theory">bifurcation theory</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20portrait" title=" phase portrait"> phase portrait</a>, <a href="https://publications.waset.org/abstracts/search?q=magnetized%20electron-positron%20plasma" title=" magnetized electron-positron plasma"> magnetized electron-positron plasma</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20Zakharov-Kuznetsov%20equation" title=" the Zakharov-Kuznetsov equation"> the Zakharov-Kuznetsov equation</a> </p> <a href="https://publications.waset.org/abstracts/72076/nonlinear-propagation-of-acoustic-soliton-waves-in-dense-quantum-electron-positron-magnetoplasma" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72076.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">243</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5235</span> Application of Strong Optical Feedback to Enhance the Modulation Bandwidth of Semiconductor Lasers to the Millimeter-Wave Band</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Moustafa%20Ahmed">Moustafa Ahmed</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20Bakry"> Ahmed Bakry</a>, <a href="https://publications.waset.org/abstracts/search?q=Fumio%20Koyama"> Fumio Koyama</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We report on the use of strong external optical feedback to enhance the modulation response of semiconductor lasers over a frequency passband around modulation frequencies higher than 60 GHz. We show that this modulation enhancement is a type of photon-photon resonance (PPR) of oscillating modes in the external cavity formed between the laser and the external reflector. The study is based on a time-delay rate equation model that takes into account both the strong feedback and multiple reflections in the external cavity. We examine the harmonic and intermodulation distortions associated with single and two-tone modulations in the mm-wave band of the resonant modulation. We show that compared with solitary lasers modulated around the carrier-photon resonance frequency, the present mm-wave modulated signal has lower distortions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=semiconductor%20laser" title="semiconductor laser">semiconductor laser</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20feedback" title=" optical feedback"> optical feedback</a>, <a href="https://publications.waset.org/abstracts/search?q=modulation" title=" modulation"> modulation</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20distortion" title=" harmonic distortion"> harmonic distortion</a> </p> <a href="https://publications.waset.org/abstracts/10588/application-of-strong-optical-feedback-to-enhance-the-modulation-bandwidth-of-semiconductor-lasers-to-the-millimeter-wave-band" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10588.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">747</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5234</span> Mapping Method to Solve a Nonlinear Schrodinger Type Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Edamana%20Vasudevan%20Krishnan">Edamana Vasudevan Krishnan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=solitons" title="solitons">solitons</a>, <a href="https://publications.waset.org/abstracts/search?q=integrability" title=" integrability"> integrability</a>, <a href="https://publications.waset.org/abstracts/search?q=metamaterials" title=" metamaterials"> metamaterials</a>, <a href="https://publications.waset.org/abstracts/search?q=mapping%20method" title=" mapping method"> mapping method</a> </p> <a href="https://publications.waset.org/abstracts/32851/mapping-method-to-solve-a-nonlinear-schrodinger-type-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32851.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">494</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5233</span> Asymptotic Expansion of the Korteweg-de Vries-Burgers Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jian-Jun%20Shu">Jian-Jun Shu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20expansion" title="asymptotic expansion">asymptotic expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equation" title=" differential equation"> differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Korteweg-de%20Vries-Burgers%20%28KdVB%29%20equation" title=" Korteweg-de Vries-Burgers (KdVB) equation"> Korteweg-de Vries-Burgers (KdVB) equation</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton" title=" soliton"> soliton</a> </p> <a href="https://publications.waset.org/abstracts/78883/asymptotic-expansion-of-the-korteweg-de-vries-burgers-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/78883.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">249</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5232</span> Analytic Solutions of Solitary Waves in Three-Level Unbalanced Dense Media</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sofiane%20Grira">Sofiane Grira</a>, <a href="https://publications.waset.org/abstracts/search?q=Hichem%20Eleuch"> Hichem Eleuch</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We explore the analytical soliton-pair solutions for unbalanced coupling between the two coherent lights and the atomic transitions in a dissipative three-level system in lambda conﬁguration. The two allowed atomic transitions are interacting resonantly with two laser ﬁelds. For unbalanced coupling, it is possible to derive an explicit solution for non-linear differential equations describing the soliton-pair propagation in this three-level system with the same velocity. We suppose that the spontaneous emission rates from the excited state to both ground states are the same. In this work, we focus on such case where we consider the coupling between the transitions and the optical ﬁelds are unbalanced. The existence conditions for the soliton-pair propagations are determined. We will show that there are four possible configurations of the soliton-pair pulses. Two of them can be interpreted as a couple of solitons with same directions of polarization and the other two as soliton-pair with opposite directions of polarization. Due to the fact that solitons have stable shapes while propagating in the considered media, they are insensitive to noise and dispersion. Our results have potential applications in data transfer with the soliton-pair pulses, where a dissipative three-level medium could be a realistic model for the optical communication media. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20differential%20equations" title="non-linear differential equations">non-linear differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=solitons" title=" solitons"> solitons</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20propagations" title=" wave propagations"> wave propagations</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20fiber" title=" optical fiber"> optical fiber</a> </p> <a href="https://publications.waset.org/abstracts/108578/analytic-solutions-of-solitary-waves-in-three-level-unbalanced-dense-media" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/108578.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">136</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5231</span> Local Radial Basis Functions for Helmholtz Equation in Seismic Inversion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hebert%20Montegranario">Hebert Montegranario</a>, <a href="https://publications.waset.org/abstracts/search?q=Mauricio%20Londo%C3%B1o"> Mauricio Londoño </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Helmholtz%20equation" title="Helmholtz equation">Helmholtz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=meshless%20methods" title=" meshless methods"> meshless methods</a>, <a href="https://publications.waset.org/abstracts/search?q=seismic%20imaging" title=" seismic imaging"> seismic imaging</a>, <a href="https://publications.waset.org/abstracts/search?q=wavefield%20inversion" title=" wavefield inversion"> wavefield inversion</a> </p> <a href="https://publications.waset.org/abstracts/33679/local-radial-basis-functions-for-helmholtz-equation-in-seismic-inversion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33679.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">547</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5230</span> The Construction of Exact Solutions for the Nonlinear Lattice Equation via Coth and Csch Functions Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Zerarka">A. Zerarka</a>, <a href="https://publications.waset.org/abstracts/search?q=W.%20Djoudi"> W. Djoudi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coth%20functions" title="coth functions">coth functions</a>, <a href="https://publications.waset.org/abstracts/search?q=csch%20functions" title=" csch functions"> csch functions</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20partial%20differential%20equation" title=" nonlinear partial differential equation"> nonlinear partial differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=travelling%20wave%20solutions" title=" travelling wave solutions"> travelling wave solutions</a> </p> <a href="https://publications.waset.org/abstracts/20374/the-construction-of-exact-solutions-for-the-nonlinear-lattice-equation-via-coth-and-csch-functions-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20374.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">662</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5229</span> Symbolic Computation on Variable-Coefficient Non-Linear Dispersive Wave Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Edris%20Rawashdeh">Edris Rawashdeh</a>, <a href="https://publications.waset.org/abstracts/search?q=I.%20Abu-Falahah"> I. Abu-Falahah</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20M.%20Jaradat"> H. M. Jaradat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The variable-coefficient non-linear dispersive wave equation is investigated with the aid of symbolic computation. By virtue of a newly developed simplified bilinear method, multi-soliton solutions for such an equation have been derived. Effects of the inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed with the aid of the characteristic curve method and graphical analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dispersive%20wave%20equations" title="dispersive wave equations">dispersive wave equations</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20soliton%20solution" title=" multiple soliton solution"> multiple soliton solution</a>, <a href="https://publications.waset.org/abstracts/search?q=Hirota%20Bilinear%20Method" title=" Hirota Bilinear Method"> Hirota Bilinear Method</a>, <a href="https://publications.waset.org/abstracts/search?q=symbolic%20computation" title=" symbolic computation"> symbolic computation</a> </p> <a href="https://publications.waset.org/abstracts/18831/symbolic-computation-on-variable-coefficient-non-linear-dispersive-wave-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18831.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">456</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=solitary%20wave%20solutions&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=solitary%20wave%20solutions&page=3">3</a></li> <li class="page-item"><a class="page-link" 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