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<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>Search results for: SDNLSE - saturable discrete non linear Schrodinger equation</title> <meta name="description" content="Search results for: SDNLSE - saturable discrete non linear Schrodinger equation"> <meta name="keywords" content="SDNLSE - saturable discrete non linear Schrodinger equation"> <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 d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="SDNLSE - 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saturable discrete non linear Schrodinger equation"> <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> 5659</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: SDNLSE - saturable discrete non linear Schrodinger equation</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">5659</span> Analytical Solution of Non–Autonomous Discrete Non-Linear Schrodinger Equation With Saturable Non-Linearity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mishu%20Gupta">Mishu Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=Rama%20Gupta"> Rama Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=B-E-Bose-Einstein" title="B-E-Bose-Einstein">B-E-Bose-Einstein</a>, <a href="https://publications.waset.org/abstracts/search?q=DNLSE-Discrete%20non%20linear%20schrodinger%20equation" title=" DNLSE-Discrete non linear schrodinger equation"> DNLSE-Discrete non linear schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=NLSE-non%20linear%20schrodinger%20equation" title=" NLSE-non linear schrodinger equation"> NLSE-non linear schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=SDNLSE%20-%20saturable%20discrete%20non%20linear%20Schrodinger%20equation" title=" SDNLSE - saturable discrete non linear Schrodinger equation"> SDNLSE - saturable discrete non linear Schrodinger equation</a> </p> <a href="https://publications.waset.org/abstracts/121074/analytical-solution-of-non-autonomous-discrete-non-linear-schrodinger-equation-with-saturable-non-linearity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/121074.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">155</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">5658</span> Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Emad%20K.%20Jaradat">Emad K. Jaradat</a>, <a href="https://publications.waset.org/abstracts/search?q=Ala%E2%80%99a%20Al-Faqih"> Ala’a Al-Faqih</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20Schrodinger%20equation" title="non-linear Schrodinger equation">non-linear Schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Elzaki%20decomposition%20method" title=" Elzaki decomposition method"> Elzaki decomposition method</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20oscillator" title=" harmonic oscillator"> harmonic oscillator</a>, <a href="https://publications.waset.org/abstracts/search?q=one%20and%20two-dimensional%20Schrodinger%20equation" title=" one and two-dimensional Schrodinger equation"> one and two-dimensional Schrodinger equation</a> </p> <a href="https://publications.waset.org/abstracts/102537/approximate-solution-to-non-linear-schrodinger-equation-with-harmonic-oscillator-by-elzaki-decomposition-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/102537.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">187</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">5657</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">5656</span> On the Grid Technique by Approximating the Derivatives of the Solution of the Dirichlet Problems for (1+1) Dimensional Linear Schrodinger Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lawrence%20A.%20Farinola">Lawrence A. Farinola</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximation%20of%20derivatives" title="approximation of derivatives">approximation of derivatives</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20method" title=" finite difference method"> finite difference method</a>, <a href="https://publications.waset.org/abstracts/search?q=Schr%C3%B6dinger%20equation" title=" Schrödinger equation"> Schrödinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=uniform%20error" title=" uniform error"> uniform error</a> </p> <a href="https://publications.waset.org/abstracts/99442/on-the-grid-technique-by-approximating-the-derivatives-of-the-solution-of-the-dirichlet-problems-for-11-dimensional-linear-schrodinger-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99442.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">120</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">5655</span> The Physics of Turbulence Generation in a Fluid: Numerical Investigation Using a 1D Damped-MNLS Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Praveen%20Kumar">Praveen Kumar</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Uma"> R. Uma</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20P.%20Sharma"> R. P. Sharma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study investigates the generation of turbulence in a deep-fluid environment using a damped 1D-modified nonlinear Schrödinger equation model. The well-known damped modified nonlinear Schrödinger equation (d-MNLS) is solved using numerical methods. Artificial damping is added to the MNLS equation, and turbulence generation is investigated through a numerical simulation. The numerical simulation employs a finite difference method for temporal evolution and a pseudo-spectral approach to characterize spatial patterns. The results reveal a recurring periodic pattern in both space and time when the nonlinear Schrödinger equation is considered. Additionally, the study shows that the modified nonlinear Schrödinger equation disrupts the localization of structure and the recurrence of the Fermi-Pasta-Ulam (FPU) phenomenon. The energy spectrum exhibits a power-law behavior, closely following Kolmogorov's spectra steeper than k⁻⁵/³ in the inertial sub-range. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=water%20waves" title="water waves">water waves</a>, <a href="https://publications.waset.org/abstracts/search?q=modulation%20instability" title=" modulation instability"> modulation instability</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrodynamics" title=" hydrodynamics"> hydrodynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20Schr%C3%B6dinger%27s%20equation" title=" nonlinear Schrödinger's equation"> nonlinear Schrödinger's equation</a> </p> <a href="https://publications.waset.org/abstracts/179074/the-physics-of-turbulence-generation-in-a-fluid-numerical-investigation-using-a-1d-damped-mnls-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/179074.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">72</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">5654</span> Closed Form Exact Solution for Second Order Linear Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saeed%20Otarod">Saeed Otarod</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=explicit" title="explicit">explicit</a>, <a href="https://publications.waset.org/abstracts/search?q=linear" title=" linear"> linear</a>, <a href="https://publications.waset.org/abstracts/search?q=differential" title=" differential"> differential</a>, <a href="https://publications.waset.org/abstracts/search?q=closed%20form" title=" closed form"> closed form</a> </p> <a href="https://publications.waset.org/abstracts/185365/closed-form-exact-solution-for-second-order-linear-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/185365.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">62</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">5653</span> A Trapezoidal-Like Integrator for the Numerical Solution of One-Dimensional Time Dependent Schrödinger Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Johnson%20Oladele%20Fatokun">Johnson Oladele Fatokun</a>, <a href="https://publications.waset.org/abstracts/search?q=I.%20P.%20Akpan"> I. P. Akpan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Schrodinger%E2%80%99s%20equation" title="Schrodinger’s equation">Schrodinger’s equation</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title=" partial differential equations"> partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=method%20of%20lines%20%28MOL%29" title=" method of lines (MOL)"> method of lines (MOL)</a>, <a href="https://publications.waset.org/abstracts/search?q=stiff%20ODE" title=" stiff ODE"> stiff ODE</a>, <a href="https://publications.waset.org/abstracts/search?q=trapezoidal-like%20integrator" title=" trapezoidal-like integrator "> trapezoidal-like integrator </a> </p> <a href="https://publications.waset.org/abstracts/11665/a-trapezoidal-like-integrator-for-the-numerical-solution-of-one-dimensional-time-dependent-schrodinger-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11665.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">418</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">5652</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">5651</span> The Soliton Solution of the Quadratic-Cubic Nonlinear Schrodinger Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sarun%20Phibanchon">Sarun Phibanchon</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuttakarn%20Rattanachai"> Yuttakarn Rattanachai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=soliton" title="soliton">soliton</a>, <a href="https://publications.waset.org/abstracts/search?q=ion-acoustic%20waves" title=" ion-acoustic waves"> ion-acoustic waves</a>, <a href="https://publications.waset.org/abstracts/search?q=plasma" title=" plasma"> plasma</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a> </p> <a href="https://publications.waset.org/abstracts/32663/the-soliton-solution-of-the-quadratic-cubic-nonlinear-schrodinger-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32663.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">411</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">5650</span> Fundamental Solutions for Discrete Dynamical Systems Involving the Fractional Laplacian</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jorge%20Gonzalez%20Camus">Jorge Gonzalez Camus</a>, <a href="https://publications.waset.org/abstracts/search?q=Valentin%20Keyantuo"> Valentin Keyantuo</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahamadi%20Warma"> Mahamadi Warma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20fractional%20Laplacian" title="discrete fractional Laplacian">discrete fractional Laplacian</a>, <a href="https://publications.waset.org/abstracts/search?q=explicit%20representation%20of%20solutions" title=" explicit representation of solutions"> explicit representation of solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20heat%20and%20wave%20equations" title=" fractional heat and wave equations"> fractional heat and wave equations</a>, <a href="https://publications.waset.org/abstracts/search?q=fundamental" title=" fundamental"> fundamental</a> </p> <a href="https://publications.waset.org/abstracts/99922/fundamental-solutions-for-discrete-dynamical-systems-involving-the-fractional-laplacian" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99922.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">209</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">5649</span> A Study of Non Linear Partial Differential Equation with Random Initial Condition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayaz%20Ahmad">Ayaz Ahmad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=drift%20term" title="drift term">drift term</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20time%20blow%20up" title=" finite time blow up"> finite time blow up</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20problem" title=" inverse problem"> inverse problem</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/77445/a-study-of-non-linear-partial-differential-equation-with-random-initial-condition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77445.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">215</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">5648</span> Relativistic Energy Analysis for Some q Deformed Shape Invariant Potentials in D Dimensions Using SUSYQM Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Suparmi">A. Suparmi</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20Cari"> C. Cari</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Yunianto"> M. Yunianto</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20N.%20Pratiwi"> B. N. Pratiwi </a> </p> <p class="card-text"><strong>Abstract:</strong></p> D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=D-dimensional%20dirac%20equation" title="D-dimensional dirac equation">D-dimensional dirac equation</a>, <a href="https://publications.waset.org/abstracts/search?q=non-central%20potential" title=" non-central potential"> non-central potential</a>, <a href="https://publications.waset.org/abstracts/search?q=SUSY%20QM" title=" SUSY QM"> SUSY QM</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20wave%20function" title=" radial wave function"> radial wave function</a> </p> <a href="https://publications.waset.org/abstracts/43601/relativistic-energy-analysis-for-some-q-deformed-shape-invariant-potentials-in-d-dimensions-using-susyqm-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43601.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">344</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">5647</span> Mode-Locked Fiber Laser Using Charcoal and Graphene Saturable Absorbers to Generate 20-GHz and 50-GHz Pulse Trains, Respectively</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ashiq%20Rahman">Ashiq Rahman</a>, <a href="https://publications.waset.org/abstracts/search?q=Sunil%20Thapa"> Sunil Thapa</a>, <a href="https://publications.waset.org/abstracts/search?q=Shunyao%20Fan"> Shunyao Fan</a>, <a href="https://publications.waset.org/abstracts/search?q=Niloy%20K.%20Dutta"> Niloy K. Dutta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A 20-GHz and a 50-GHz pulse train are generated using a fiber ring laser setup that incorporates Rational Harmonic Mode Locking. Two separate experiments were carried out using charcoal nanoparticles and graphene nanoparticles acting as saturable absorbers to reduce the pulse width generated from rational harmonic mode-locking (RHML). Autocorrelator trace shows that the pulse width is reduced from 5.6-ps to 3.2-ps using charcoal at 20-GHz, and to 2.7-ps using graphene at 50-GHz repetition rates, which agrees with the simulation findings. Numerical simulations have been carried out to study the effect of varying the linear and nonlinear absorbance parameters of both absorbers on output pulse widths. Experiments closely agree with the simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fiber%20optics" title="fiber optics">fiber optics</a>, <a href="https://publications.waset.org/abstracts/search?q=fiber%20lasers" title=" fiber lasers"> fiber lasers</a>, <a href="https://publications.waset.org/abstracts/search?q=mode%20locking" title=" mode locking"> mode locking</a>, <a href="https://publications.waset.org/abstracts/search?q=saturable%20absorbers" title=" saturable absorbers"> saturable absorbers</a> </p> <a href="https://publications.waset.org/abstracts/157130/mode-locked-fiber-laser-using-charcoal-and-graphene-saturable-absorbers-to-generate-20-ghz-and-50-ghz-pulse-trains-respectively" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/157130.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">97</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">5646</span> Analytical Solutions to the N-Dimensional Schrödinger Equation with a Collective Potential Model to Study Energy Spectra Andthermodynamic Properties of Selected Diatomic Molecules</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=BenedictI%20Ita">BenedictI Ita</a>, <a href="https://publications.waset.org/abstracts/search?q=Etido%20P.%20Inyang"> Etido P. Inyang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, the resolutions of the N-dimensional Schrödinger equation with the screened modified Kratzerplus inversely quadratic Yukawa potential (SMKIQYP) have been obtained with the Greene-Aldrich approximation scheme using the Nikiforov-Uvarov method. The eigenvalues and the normalized eigenfunctions are obtained. We then apply the energy spectrum to study four (HCl, N₂, NO, and CO) diatomic molecules. The results show that the energy spectra of these diatomic molecules increase as quantum numbers increase. The energy equation was also used to calculate the partition function and other thermodynamic properties. We predicted the partition function of CO and NO. To check the accuracy of our work, the special case (Modified Kratzer and screened Modified Kratzer potentials) of the collective potential energy eigenvalues agrees excellently with the existing literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Schr%C3%B6dinger%20equation" title="Schrödinger equation">Schrödinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Nikiforov-Uvarov%20method" title=" Nikiforov-Uvarov method"> Nikiforov-Uvarov method</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20screened%20Kratzer" title=" modified screened Kratzer"> modified screened Kratzer</a>, <a href="https://publications.waset.org/abstracts/search?q=inversely%20quadratic%20Yukawa%20potential" title=" inversely quadratic Yukawa potential"> inversely quadratic Yukawa potential</a>, <a href="https://publications.waset.org/abstracts/search?q=diatomic%20molecules" title=" diatomic molecules"> diatomic molecules</a> </p> <a href="https://publications.waset.org/abstracts/152962/analytical-solutions-to-the-n-dimensional-schrodinger-equation-with-a-collective-potential-model-to-study-energy-spectra-andthermodynamic-properties-of-selected-diatomic-molecules" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/152962.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">84</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">5645</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">5644</span> Energy States of Some Diatomic Molecules: Exact Quantization Rule Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Babatunde%20J.%20Falaye">Babatunde J. Falaye</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, we obtain the approximate analytical solutions of the radial Schrödinger equation for the Deng-Fan diatomic molecular potential by using exact quantization rule approach. The wave functions have been expressed by hypergeometric functions via the functional analysis approach. An extension to rotational-vibrational energy eigenvalues of some diatomic molecules are also presented. It is shown that the calculated energy levels are in good agreement with the ones obtained previously E_nl-D (shifted Deng-Fan). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Schr%C3%B6dinger%20equation" title="Schrödinger equation">Schrödinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20quantization%20rule" title=" exact quantization rule"> exact quantization rule</a>, <a href="https://publications.waset.org/abstracts/search?q=functional%20analysis" title=" functional analysis"> functional analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=Deng-Fan%20potential" title=" Deng-Fan potential"> Deng-Fan potential</a> </p> <a href="https://publications.waset.org/abstracts/17622/energy-states-of-some-diatomic-molecules-exact-quantization-rule-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17622.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">499</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">5643</span> Inverse Saturable Absorption in Non-linear Amplifying Loop Mirror Mode-Locked Fiber Laser</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haobin%20Zheng">Haobin Zheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Xiang%20Zhang"> Xiang Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Yong%20Shen"> Yong Shen</a>, <a href="https://publications.waset.org/abstracts/search?q=Hongxin%20Zou"> Hongxin Zou</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The research focuses on mode-locked fiber lasers with a non-linear amplifying loop mirror (NALM). Although these lasers have shown potential, they still have limitations in terms of low repetition rate. The self-starting of mode-locking in NALM is influenced by the cross-phase modulation (XPM) effect, which has not been thoroughly studied. The aim of this study is two-fold. First, to overcome the difficulties associated with increasing the repetition rate in mode-locked fiber lasers with NALM. Second, to analyze the influence of XPM on self-starting of mode-locking. The power distributions of two counterpropagating beams in the NALM and the differential non-linear phase shift (NPS) accumulations are calculated. The analysis is conducted from the perspective of NPS accumulation. The differential NPSs for continuous wave (CW) light and pulses in the fiber loop are compared to understand the inverse saturable absorption (ISA) mechanism during pulse formation in NALM. The study reveals a difference in differential NPSs between CW light and pulses in the fiber loop in NALM. This difference leads to an ISA mechanism, which has not been extensively studied in artificial saturable absorbers. The ISA in NALM provides an explanation for experimentally observed phenomena, such as active mode-locking initiation through tapping the fiber or fine-tuning light polarization. These findings have important implications for optimizing the design of NALM and reducing the self-starting threshold of high-repetition-rate mode-locked fiber lasers. This study contributes to the theoretical understanding of NALM mode-locked fiber lasers by exploring the ISA mechanism and its impact on self-starting of mode-locking. The research fills a gap in the existing knowledge regarding the XPM effect in NALM and its role in pulse formation. This study provides insights into the ISA mechanism in NALM mode-locked fiber lasers and its role in selfstarting of mode-locking. The findings contribute to the optimization of NALM design and the reduction of self-starting threshold, which are essential for achieving high-repetition-rate operation in fiber lasers. Further research in this area can lead to advancements in the field of mode-locked fiber lasers with NALM. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inverse%20saturable%20absorption" title="inverse saturable absorption">inverse saturable absorption</a>, <a href="https://publications.waset.org/abstracts/search?q=NALM" title=" NALM"> NALM</a>, <a href="https://publications.waset.org/abstracts/search?q=mode-locking" title=" mode-locking"> mode-locking</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20phase%20shift" title=" non-linear phase shift"> non-linear phase shift</a> </p> <a href="https://publications.waset.org/abstracts/173606/inverse-saturable-absorption-in-non-linear-amplifying-loop-mirror-mode-locked-fiber-laser" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/173606.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">101</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">5642</span> Dynamics of Light Induced Current in 1D Coupled Quantum Dots</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tokuei%20Sako">Tokuei Sako</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Laser-induced current in a quasi-one-dimensional nanostructure has been studied by a model of a few electrons confined in a 1D electrostatic potential coupled to electrodes at both ends and subjected to a pulsed laser field. The time-propagation of the one- and two-electron wave packets has been calculated by integrating the time-dependent Schrödinger equation directly by the symplectic integrator method with uniform Fourier grid. The temporal behavior of the resultant light-induced current in the studied systems has been discussed with respect to the lifetime of the quasi-bound states formed when the static bias voltage is applied. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pulsed%20laser%20field" title="pulsed laser field">pulsed laser field</a>, <a href="https://publications.waset.org/abstracts/search?q=nanowire" title=" nanowire"> nanowire</a>, <a href="https://publications.waset.org/abstracts/search?q=electron%20wave%20packet" title=" electron wave packet"> electron wave packet</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum%20dots" title=" quantum dots"> quantum dots</a>, <a href="https://publications.waset.org/abstracts/search?q=time-dependent%20Schr%C3%B6dinger%20equation" title=" time-dependent Schrödinger equation"> time-dependent Schrödinger equation</a> </p> <a href="https://publications.waset.org/abstracts/22996/dynamics-of-light-induced-current-in-1d-coupled-quantum-dots" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22996.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">356</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">5641</span> Exact Solutions of Discrete Sine-Gordon Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chao-Qing%20Dai">Chao-Qing Dai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=exact%20solutions" title="exact solutions">exact solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=variable-coefficient%20Jacobian%20elliptic%20function%20method" title=" variable-coefficient Jacobian elliptic function method"> variable-coefficient Jacobian elliptic function method</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20sine-Gordon%20equation" title=" discrete sine-Gordon equation"> discrete sine-Gordon equation</a>, <a href="https://publications.waset.org/abstracts/search?q=dynamical%20behaviors" title=" dynamical behaviors"> dynamical behaviors</a> </p> <a href="https://publications.waset.org/abstracts/48966/exact-solutions-of-discrete-sine-gordon-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48966.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">420</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">5640</span> Broadband Platinum Disulfide Based Saturable Absorber Used for Optical Fiber Mode Locking Lasers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hui%20Long">Hui Long</a>, <a href="https://publications.waset.org/abstracts/search?q=Chun%20Yin%20Tang"> Chun Yin Tang</a>, <a href="https://publications.waset.org/abstracts/search?q=Ping%20Kwong%20Cheng"> Ping Kwong Cheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Xin%20Yu%20Wang"> Xin Yu Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Wayesh%20Qarony"> Wayesh Qarony</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuen%20Hong%20Tsang"> Yuen Hong Tsang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Two dimensional (2D) materials have recently attained substantial research interest since the discovery of graphene. However, the zero-bandgap feature of the graphene limits its nonlinear optical applications, e.g., saturable absorption for these applications require strong light-matter interaction. Nevertheless, the excellent optoelectronic properties, such as broad tunable bandgap energy and high carrier mobility of Group 10 transition metal dichalcogenides 2D materials, e.g., PtS2 introduce new degree of freedoms in the optoelectronic applications. This work reports our recent research findings regarding the saturable absorption property of PtS2 layered 2D material and its possibility to be used as saturable absorber (SA) for ultrafast mode locking fiber laser. The demonstration of mode locking operation by using the fabricated PtS2 as SA will be discussed. The PtS2/PVA SA used in this experiment is made up of some few layered PtS2 nanosheets fabricated via a simple ultrasonic liquid exfoliation. The operational wavelength located at ~1 micron is demonstrated from Yb-doped mode locking fiber laser ring cavity by using the PtS2 SA. The fabricated PtS2 saturable absorber offers strong nonlinear properties, and it is capable of producing regular mode locking laser pulses with pulse to pulse duration matched with the round-trip cavity time. The results confirm successful mode locking operation achieved by the fabricated PtS2 material. This work opens some new opportunities for these PtS2 materials for the ultrafast laser generation. Acknowledgments: This work is financially supported by Shenzhen Science and Technology Innovation Commission (JCYJ20170303160136888) and the Research Grants Council of Hong Kong, China (GRF 152109/16E, PolyU code: B-Q52T). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=platinum%20disulfide" title="platinum disulfide">platinum disulfide</a>, <a href="https://publications.waset.org/abstracts/search?q=PtS2" title=" PtS2"> PtS2</a>, <a href="https://publications.waset.org/abstracts/search?q=saturable%20absorption" title=" saturable absorption"> saturable absorption</a>, <a href="https://publications.waset.org/abstracts/search?q=saturable%20absorber" title=" saturable absorber"> saturable absorber</a>, <a href="https://publications.waset.org/abstracts/search?q=mode%20locking%20laser" title=" mode locking laser"> mode locking laser</a> </p> <a href="https://publications.waset.org/abstracts/102303/broadband-platinum-disulfide-based-saturable-absorber-used-for-optical-fiber-mode-locking-lasers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/102303.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">188</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">5639</span> Optimization of Fourth Order Discrete-Approximation Inclusions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elimhan%20N.%20Mahmudov">Elimhan N. Mahmudov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper concerns the necessary and sufficient conditions of optimality for Cauchy problem of fourth order discrete (PD) and discrete-approximate (PDA) inclusions. The main problem is formulation of the fourth order adjoint discrete and discrete-approximate inclusions and transversality conditions, which are peculiar to problems including fourth order derivatives and approximate derivatives. Thus the necessary and sufficient conditions of optimality are obtained incorporating the Euler-Lagrange and Hamiltonian forms of inclusions. Derivation of optimality conditions are based on the apparatus of locally adjoint mapping (LAM). Moreover in the application of these results we consider the fourth order linear discrete and discrete-approximate inclusions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=difference" title="difference">difference</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=fourth" title=" fourth"> fourth</a>, <a href="https://publications.waset.org/abstracts/search?q=approximation" title=" approximation"> approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=transversality" title=" transversality"> transversality</a> </p> <a href="https://publications.waset.org/abstracts/25199/optimization-of-fourth-order-discrete-approximation-inclusions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/25199.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">374</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">5638</span> Existence and Concentration of Solutions for a Class of Elliptic Partial Differential Equations Involving p-Biharmonic Operator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Debajyoti%20Choudhuri">Debajyoti Choudhuri</a>, <a href="https://publications.waset.org/abstracts/search?q=Ratan%20Kumar%20Giri"> Ratan Kumar Giri</a>, <a href="https://publications.waset.org/abstracts/search?q=Shesadev%20Pradhan"> Shesadev Pradhan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=p-Laplacian" title="p-Laplacian">p-Laplacian</a>, <a href="https://publications.waset.org/abstracts/search?q=p-biharmonic" title=" p-biharmonic"> p-biharmonic</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20PDEs" title=" elliptic PDEs"> elliptic PDEs</a>, <a href="https://publications.waset.org/abstracts/search?q=Concentration%20lemma" title=" Concentration lemma"> Concentration lemma</a>, <a href="https://publications.waset.org/abstracts/search?q=Sobolev%20space" title=" Sobolev space"> Sobolev space</a> </p> <a href="https://publications.waset.org/abstracts/58393/existence-and-concentration-of-solutions-for-a-class-of-elliptic-partial-differential-equations-involving-p-biharmonic-operator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58393.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">234</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">5637</span> Solution of the Nonrelativistic Radial Wave Equation of Hydrogen Atom Using the Green's Function Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=F.%20U.%20Rahman">F. U. Rahman</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Q.%20Zhang"> R. Q. Zhang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work aims to develop a systematic numerical technique which can be easily extended to many-body problem. The Lippmann Schwinger equation (integral form of the Schrodinger wave equation) is solved for the nonrelativistic radial wave of hydrogen atom using iterative integration scheme. As the unknown wave function appears on both sides of the Lippmann Schwinger equation, therefore an approximate wave function is used in order to solve the equation. The Green’s function is obtained by the method of Laplace transform for the radial wave equation with excluded potential term. Using the Lippmann Schwinger equation, the product of approximate wave function, the Green’s function and the potential term is integrated iteratively. Finally, the wave function is normalized and plotted against the standard radial wave for comparison. The outcome wave function converges to the standard wave function with the increasing number of iteration. Results are verified for the first fifteen states of hydrogen atom. The method is efficient and consistent and can be applied to complex systems in future. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Green%E2%80%99s%20function" title="Green’s function">Green’s function</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrogen%20atom" title=" hydrogen atom"> hydrogen atom</a>, <a href="https://publications.waset.org/abstracts/search?q=Lippmann%20Schwinger%20equation" title=" Lippmann Schwinger equation"> Lippmann Schwinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=radial%20wave" title=" radial wave"> radial wave</a> </p> <a href="https://publications.waset.org/abstracts/42682/solution-of-the-nonrelativistic-radial-wave-equation-of-hydrogen-atom-using-the-greens-function-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42682.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">394</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">5636</span> Discrete Sliding Modes Regulator with Exponential Holder for Non-Linear Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=G.%20Obregon-Pulido">G. Obregon-Pulido </a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20C.%20Solis-Perales"> G. C. Solis-Perales</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20A.%20Meda-Campa%C3%B1a"> J. A. Meda-Campaña</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a sliding mode controller in discrete time. The design of the controller is based on the theory of regulation for nonlinear systems. In the problem of disturbance rejection and/or output tracking, it is known that in discrete time, a controller that uses the zero-order holder only guarantees tracking at the sampling instances but not between instances. It is shown that using the so-called exponential holder, it is possible to guarantee asymptotic zero output tracking error, also between the sampling instant. For stabilizing the problem of close loop system we introduce the sliding mode approach relaxing the requirements of the existence of a linear stabilizing control law. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=regulation%20theory" title="regulation theory">regulation theory</a>, <a href="https://publications.waset.org/abstracts/search?q=sliding%20modes" title=" sliding modes"> sliding modes</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20controller" title=" discrete controller"> discrete controller</a>, <a href="https://publications.waset.org/abstracts/search?q=ripple-free%20tracking" title=" ripple-free tracking"> ripple-free tracking</a> </p> <a href="https://publications.waset.org/abstracts/178771/discrete-sliding-modes-regulator-with-exponential-holder-for-non-linear-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/178771.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">54</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">5635</span> Computational Simulations on Stability of Model Predictive Control for Linear Discrete-Time Stochastic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tomoaki%20Hashimoto">Tomoaki Hashimoto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and a moving terminal time. This paper examines the stability of model predictive control for linear discrete-time systems with additive stochastic disturbances. A sufficient condition for the stability of the closed-loop system with model predictive control is derived by means of a linear matrix inequality. The objective of this paper is to show the results of computational simulations in order to verify the validity of the obtained stability condition. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=computational%20simulations" title="computational simulations">computational simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title=" optimal control"> optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=predictive%20control" title=" predictive control"> predictive control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20systems" title=" stochastic systems"> stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20systems" title=" discrete-time systems"> discrete-time systems</a> </p> <a href="https://publications.waset.org/abstracts/35462/computational-simulations-on-stability-of-model-predictive-control-for-linear-discrete-time-stochastic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35462.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">432</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">5634</span> Numerical Simulations on Feasibility of Stochastic Model Predictive Control for Linear Discrete-Time Systems with Random Dither Quantization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Taiki%20Baba">Taiki Baba</a>, <a href="https://publications.waset.org/abstracts/search?q=Tomoaki%20Hashimoto"> Tomoaki Hashimoto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The random dither quantization method enables us to achieve much better performance than the simple uniform quantization method for the design of quantized control systems. Motivated by this fact, the stochastic model predictive control method in which a performance index is minimized subject to probabilistic constraints imposed on the state variables of systems has been proposed for linear feedback control systems with random dither quantization. In other words, a method for solving optimal control problems subject to probabilistic state constraints for linear discrete-time control systems with random dither quantization has been already established. To our best knowledge, however, the feasibility of such a kind of optimal control problems has not yet been studied. Our objective in this paper is to investigate the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization. To this end, we provide the results of numerical simulations that verify the feasibility of stochastic model predictive control problems for linear discrete-time control systems with random dither quantization. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=model%20predictive%20control" title="model predictive control">model predictive control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20systems" title=" stochastic systems"> stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=probabilistic%20constraints" title=" probabilistic constraints"> probabilistic constraints</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20dither%20quantization" title=" random dither quantization"> random dither quantization</a> </p> <a href="https://publications.waset.org/abstracts/78538/numerical-simulations-on-feasibility-of-stochastic-model-predictive-control-for-linear-discrete-time-systems-with-random-dither-quantization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/78538.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">282</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">5633</span> Stochastic Model Predictive Control for Linear Discrete-Time Systems with Random Dither Quantization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tomoaki%20Hashimoto">Tomoaki Hashimoto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Recently, feedback control systems using random dither quantizers have been proposed for linear discrete-time systems. However, the constraints imposed on state and control variables have not yet been taken into account for the design of feedback control systems with random dither quantization. Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. An important advantage of model predictive control is its ability to handle constraints imposed on state and control variables. Based on the model predictive control approach, the objective of this paper is to present a control method that satisfies probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization. In other words, this paper provides a method for solving the optimal control problems subject to probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title="optimal control">optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20systems" title=" stochastic systems"> stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20dither" title=" random dither"> random dither</a>, <a href="https://publications.waset.org/abstracts/search?q=quantization" title=" quantization"> quantization</a> </p> <a href="https://publications.waset.org/abstracts/63970/stochastic-model-predictive-control-for-linear-discrete-time-systems-with-random-dither-quantization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63970.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">444</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">5632</span> Stability of Hybrid Stochastic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manlika%20Ratchagit">Manlika Ratchagit</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=robust%20mean%20square%20stability" title="robust mean square stability">robust mean square stability</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20stochastic%20systems" title=" discrete-time stochastic systems"> discrete-time stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20systems" title=" hybrid systems"> hybrid systems</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20time-varying%20delays" title=" interval time-varying delays"> interval time-varying delays</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20functional" title=" Lyapunov functional"> Lyapunov functional</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities" title=" linear matrix inequalities"> linear matrix inequalities</a> </p> <a href="https://publications.waset.org/abstracts/20283/stability-of-hybrid-stochastic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20283.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">485</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">5631</span> New Results on Stability of Hybrid Stochastic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manlika%20Rajchakit">Manlika Rajchakit</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=robust%20mean%20square%20stability" title="robust mean square stability">robust mean square stability</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20stochastic%20systems" title=" discrete-time stochastic systems"> discrete-time stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20systems" title=" hybrid systems"> hybrid systems</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20time-varying%20delays" title=" interval time-varying delays"> interval time-varying delays</a>, <a href="https://publications.waset.org/abstracts/search?q=lyapunov%20functional" title=" lyapunov functional"> lyapunov functional</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities" title=" linear matrix inequalities"> linear matrix inequalities</a> </p> <a href="https://publications.waset.org/abstracts/19809/new-results-on-stability-of-hybrid-stochastic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19809.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">429</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">5630</span> Decomposition of Third-Order Discrete-Time Linear Time-Varying Systems into Its Second- and First-Order Pairs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Hassan%20Abdullahi">Mohamed Hassan Abdullahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Decomposition is used as a synthesis tool in several physical systems. It can also be used for tearing and restructuring, which is large-scale system analysis. On the other hand, the commutativity of series-connected systems has fascinated the interest of researchers, and its advantages have been emphasized in the literature. The presentation looks into the necessary conditions for decomposing any third-order discrete-time linear time-varying system into a commutative pair of first- and second-order systems. Additional requirements are derived in the case of nonzero initial conditions. MATLAB simulations are used to verify the findings. The work is unique and is being published for the first time. It is critical from the standpoints of synthesis and/or design. Because many design techniques in engineering systems rely on tearing and reconstruction, this is the process of putting together simple components to create a finished product. Furthermore, it is demonstrated that regarding sensitivity to initial conditions, some combinations may be better than others. The results of this work can be extended for the decomposition of fourth-order discrete-time linear time-varying systems into lower-order commutative pairs, as two second-order commutative subsystems or one first-order and one third-order commutative subsystems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=commutativity" title="commutativity">commutativity</a>, <a href="https://publications.waset.org/abstracts/search?q=decomposition" title=" decomposition"> decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete%20time-varying%20systems" title=" discrete time-varying systems"> discrete time-varying systems</a>, <a href="https://publications.waset.org/abstracts/search?q=systems" title=" systems"> systems</a> </p> <a href="https://publications.waset.org/abstracts/151285/decomposition-of-third-order-discrete-time-linear-time-varying-systems-into-its-second-and-first-order-pairs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/151285.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">110</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=SDNLSE%20-%20saturable%20discrete%20non%20linear%20Schrodinger%20equation&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=SDNLSE%20-%20saturable%20discrete%20non%20linear%20Schrodinger%20equation&page=3">3</a></li> <li class="page-item"><a class="page-link" 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