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Vries-Burgers (KdVB) equation</title> <meta name="description" content="Search results for: Korteweg-de Vries-Burgers (KdVB) equation"> <meta name="keywords" content="Korteweg-de Vries-Burgers (KdVB) 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 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<form method="get" 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="Korteweg-de Vries-Burgers (KdVB) 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> 1982</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Korteweg-de Vries-Burgers (KdVB) equation</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1982</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">1981</span> Fokas-Lenells Equation Conserved Quantities and Landau-Lifshitz System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Riki%20Dutta">Riki Dutta</a>, <a href="https://publications.waset.org/abstracts/search?q=Sagardeep%20Talukdar"> Sagardeep Talukdar</a>, <a href="https://publications.waset.org/abstracts/search?q=Gautam%20Kumar%20Saharia"> Gautam Kumar Saharia</a>, <a href="https://publications.waset.org/abstracts/search?q=Sudipta%20Nandy"> Sudipta Nandy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fokas-Lenells equation (FLE) is one of the integrable nonlinear equations use to describe the propagation of ultrashort optical pulses in an optical medium. A 2x2 Lax pair has been introduced for the FLE and from that solving the Riccati equation yields infinitely many conserved quantities. Thereafter for a new field function (S) of the Landau-Lifshitz (LL) system, a gauge equivalence of the FLE with the generalised LL equation has been derived. We hope our findings are useful for the application purpose of FLE in optics and other branches of physics. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conserved%20quantities" title="conserved quantities">conserved quantities</a>, <a href="https://publications.waset.org/abstracts/search?q=fokas-lenells%20equation" title=" fokas-lenells equation"> fokas-lenells equation</a>, <a href="https://publications.waset.org/abstracts/search?q=landau-lifshitz%20equation" title=" landau-lifshitz equation"> landau-lifshitz equation</a>, <a href="https://publications.waset.org/abstracts/search?q=lax%20pair" title=" lax pair"> lax pair</a> </p> <a href="https://publications.waset.org/abstracts/165239/fokas-lenells-equation-conserved-quantities-and-landau-lifshitz-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165239.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> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1980</span> An Analytical Method for Solving General Riccati Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20Pala">Y. Pala</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20O.%20Ertas"> M. O. Ertas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Riccati%20equation" title="Riccati equation">Riccati equation</a>, <a href="https://publications.waset.org/abstracts/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=proper%20solution" title=" proper solution"> proper solution</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear" title=" nonlinear"> nonlinear</a> </p> <a href="https://publications.waset.org/abstracts/64988/an-analytical-method-for-solving-general-riccati-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/64988.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">354</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">1979</span> Operator Splitting Scheme for the Inverse Nagumo Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sharon-Yasotha%20Veerayah-Mcgregor">Sharon-Yasotha Veerayah-Mcgregor</a>, <a href="https://publications.waset.org/abstracts/search?q=Valipuram%20Manoranjan"> Valipuram Manoranjan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A backward or inverse problem is known to be an ill-posed problem due to its instability that easily emerges with any slight change within the conditions of the problem. Therefore, only a limited number of numerical approaches are available to solve a backward problem. This paper considers the Nagumo equation, an equation that describes impulse propagation in nerve axons, which also models population growth with the Allee effect. A creative operator splitting numerical scheme is constructed to solve the inverse Nagumo equation. Computational simulations are used to verify that this scheme is stable, accurate, and efficient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=inverse%2Fbackward%20equation" title="inverse/backward equation">inverse/backward equation</a>, <a href="https://publications.waset.org/abstracts/search?q=operator-splitting" title=" operator-splitting"> operator-splitting</a>, <a href="https://publications.waset.org/abstracts/search?q=Nagumo%20equation" title=" Nagumo equation"> Nagumo equation</a>, <a href="https://publications.waset.org/abstracts/search?q=ill-posed" title=" ill-posed"> ill-posed</a>, <a href="https://publications.waset.org/abstracts/search?q=finite-difference" title=" finite-difference"> finite-difference</a> </p> <a href="https://publications.waset.org/abstracts/182287/operator-splitting-scheme-for-the-inverse-nagumo-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182287.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">98</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">1978</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 Schr枚dinger 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">1977</span> Image Transform Based on Integral Equation-Wavelet Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang">Yuan Yan Tang</a>, <a href="https://publications.waset.org/abstracts/search?q=Lina%20Yang"> Lina Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Hong%20Li"> Hong Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20model" title="harmonic model">harmonic model</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation%20%28PDE%29" title=" partial differential equation (PDE)"> partial differential equation (PDE)</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equation" title=" integral equation"> integral equation</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20representation" title=" integral representation"> integral representation</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20measure%20formula" title=" boundary measure formula"> boundary measure formula</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20collocation" title=" wavelet collocation"> wavelet collocation</a> </p> <a href="https://publications.waset.org/abstracts/3920/image-transform-based-on-integral-equation-wavelet-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3920.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">558</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">1976</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">1975</span> Study of Cahn-Hilliard Equation to Simulate Phase Separation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nara%20Guimar%C3%A3es">Nara Guimar茫es</a>, <a href="https://publications.waset.org/abstracts/search?q=Marcelo%20Aquino%20Martorano"> Marcelo Aquino Martorano</a>, <a href="https://publications.waset.org/abstracts/search?q=Douglas%20Gouv%C3%AAa"> Douglas Gouv锚a</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cahn-Hilliard%20equation" title="Cahn-Hilliard equation">Cahn-Hilliard equation</a>, <a href="https://publications.waset.org/abstracts/search?q=miscibility%20gap" title=" miscibility gap"> miscibility gap</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20separation" title=" phase separation"> phase separation</a>, <a href="https://publications.waset.org/abstracts/search?q=dimensional%20domains" title=" dimensional domains"> dimensional domains</a> </p> <a href="https://publications.waset.org/abstracts/17579/study-of-cahn-hilliard-equation-to-simulate-phase-separation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17579.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">517</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">1974</span> Study and Solving Partial Differential Equation of Danel Equation in the Vibration Shells </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hesamoddin%20Abdollahpour">Hesamoddin Abdollahpour</a>, <a href="https://publications.waset.org/abstracts/search?q=Roghayeh%20Abdollahpour"> Roghayeh Abdollahpour</a>, <a href="https://publications.waset.org/abstracts/search?q=Elham%20Rahgozar"> Elham Rahgozar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=large%20amplitude" title="large amplitude">large amplitude</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibrations" title=" free vibrations"> free vibrations</a>, <a href="https://publications.waset.org/abstracts/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=Danell%20Equation" title=" Danell Equation"> Danell Equation</a>, <a href="https://publications.waset.org/abstracts/search?q=diagram%20of%20phase%20plane" title=" diagram of phase plane "> diagram of phase plane </a> </p> <a href="https://publications.waset.org/abstracts/66849/study-and-solving-partial-differential-equation-of-danel-equation-in-the-vibration-shells" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66849.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">320</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">1973</span> Modification of Rk Equation of State for Liquid and Vapor of Ammonia by Genetic Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Mousavian">S. Mousavian</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Mousavian"> F. Mousavian</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20Nikkhah%20Rashidabad"> V. Nikkhah Rashidabad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Cubic equations of state like Redlich鈥揔wong (RK) EOS have been proved to be very reliable tools in the prediction of phase behavior. Despite their good performance in compositional calculations, they usually suffer from weaknesses in the predictions of saturated liquid density. In this research, RK equation was modified. The result of this study shows that modified equation has good agreement with experimental data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=equation%20of%20state" title="equation of state">equation of state</a>, <a href="https://publications.waset.org/abstracts/search?q=modification" title=" modification"> modification</a>, <a href="https://publications.waset.org/abstracts/search?q=ammonia" title=" ammonia"> ammonia</a>, <a href="https://publications.waset.org/abstracts/search?q=genetic%20algorithm" title=" genetic algorithm"> genetic algorithm</a> </p> <a href="https://publications.waset.org/abstracts/2790/modification-of-rk-equation-of-state-for-liquid-and-vapor-of-ammonia-by-genetic-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2790.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">382</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">1972</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">1971</span> Divergence Regularization Method for Solving Ill-Posed Cauchy Problem for the Helmholtz Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Benedict%20Barnes">Benedict Barnes</a>, <a href="https://publications.waset.org/abstracts/search?q=Anthony%20Y.%20Aidoo"> Anthony Y. Aidoo</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=divergence%20regularization%20method" title="divergence regularization method">divergence regularization method</a>, <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=ill-posed%20inhomogeneous%20Cauchy%20boundary%20conditions" title=" ill-posed inhomogeneous Cauchy boundary conditions"> ill-posed inhomogeneous Cauchy boundary conditions</a> </p> <a href="https://publications.waset.org/abstracts/137727/divergence-regularization-method-for-solving-ill-posed-cauchy-problem-for-the-helmholtz-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/137727.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">189</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">1970</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鈥檚 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鈥檚 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鈥檚 function">Green鈥檚 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">1969</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 鈥揹e 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">1968</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 Schr枚dinger equation model. The well-known damped modified nonlinear Schr枚dinger 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 Schr枚dinger equation is considered. Additionally, the study shows that the modified nonlinear Schr枚dinger 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鈦烩伒/鲁 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 Schr枚dinger's equation"> nonlinear Schr枚dinger'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">1967</span> Exact Soliton Solutions of the Integrable (2+1)-Dimensional Fokas-Lenells Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meruyert%20Zhassybayeva">Meruyert Zhassybayeva</a>, <a href="https://publications.waset.org/abstracts/search?q=Kuralay%20Yesmukhanova"> Kuralay Yesmukhanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Ratbay%20Myrzakulov"> Ratbay Myrzakulov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Integrable nonlinear differential equations are an important class of nonlinear wave equations that admit exact soliton solutions. All these equations have an amazing property which is that their soliton waves collide elastically. One of such equations is the (1+1)-dimensional Fokas-Lenells equation. In this paper, we have constructed an integrable (2+1)-dimensional Fokas-Lenells equation. The integrability of this equation is ensured by the existence of a Lax representation for it. We obtained its bilinear form from the Hirota method. Using the Hirota method, exact one-soliton and two-soliton solutions of the (2 +1)-dimensional Fokas-Lenells equation were found. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fokas-Lenells%20equation" title="Fokas-Lenells equation">Fokas-Lenells equation</a>, <a href="https://publications.waset.org/abstracts/search?q=integrability" title=" integrability"> integrability</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton" title=" soliton"> soliton</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20Hirota%20bilinear%20method" title=" the Hirota bilinear method"> the Hirota bilinear method</a> </p> <a href="https://publications.waset.org/abstracts/99044/exact-soliton-solutions-of-the-integrable-21-dimensional-fokas-lenells-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99044.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">224</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">1966</span> Chern-Simons Equation in Financial Theory and Time-Series Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ognjen%20Vukovic">Ognjen Vukovic</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Brownian%20motion" title="Brownian motion">Brownian motion</a>, <a href="https://publications.waset.org/abstracts/search?q=Chern-Simons%20theory" title=" Chern-Simons theory"> Chern-Simons theory</a>, <a href="https://publications.waset.org/abstracts/search?q=financial%20time%20series" title=" financial time series"> financial time series</a>, <a href="https://publications.waset.org/abstracts/search?q=econophysics" title=" econophysics"> econophysics</a> </p> <a href="https://publications.waset.org/abstracts/30127/chern-simons-equation-in-financial-theory-and-time-series-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30127.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">473</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">1965</span> Fixed Point Iteration of a Damped and Unforced Duffing's Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Paschal%20A.%20Ochang">Paschal A. Ochang</a>, <a href="https://publications.waset.org/abstracts/search?q=Emmanuel%20C.%20Oji"> Emmanuel C. Oji</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Duffing鈥檚 Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing鈥檚 equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing鈥檚 Equation. We were able to identify that one can only see the fixed points to a Damped Duffing鈥檚 Equation and not to the Undamped Duffing鈥檚 Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing鈥檚 Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing鈥檚 Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing鈥檚 Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing鈥檚 equation will be reduced. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=damping" title="damping">damping</a>, <a href="https://publications.waset.org/abstracts/search?q=Duffing%27s%20equation" title=" Duffing's equation"> Duffing's equation</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point%20analysis" title=" fixed point analysis"> fixed point analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20order%20differential" title=" second order differential"> second order differential</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20analysis" title=" stability analysis"> stability analysis</a> </p> <a href="https://publications.waset.org/abstracts/72553/fixed-point-iteration-of-a-damped-and-unforced-duffings-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72553.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">292</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">1964</span> A Novel Method for Solving Nonlinear Whitham鈥揃roer鈥揔aup Equation System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayda%20Nikkar">Ayda Nikkar</a>, <a href="https://publications.waset.org/abstracts/search?q=Roghayye%20Ahmadiasl"> Roghayye Ahmadiasl</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham鈥揃roer鈥揔aup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=homotopy%20perturbation%20method" title="homotopy perturbation method">homotopy perturbation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Whitham%E2%80%93Broer%E2%80%93Kaup%20%28WBK%29%20equation" title=" Whitham鈥揃roer鈥揔aup (WBK) equation"> Whitham鈥揃roer鈥揔aup (WBK) equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Modified%20Boussinesq" title=" Modified Boussinesq"> Modified Boussinesq</a>, <a href="https://publications.waset.org/abstracts/search?q=Approximate%20Long%20Wave" title=" Approximate Long Wave"> Approximate Long Wave</a> </p> <a href="https://publications.waset.org/abstracts/35317/a-novel-method-for-solving-nonlinear-whitham-broer-kaup-equation-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35317.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">311</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">1963</span> Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sachin%20Kumar">Sachin Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20PDE" title="fractional PDE">fractional PDE</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20valued%20function" title=" fuzzy valued function"> fuzzy valued function</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20equation" title=" diffusion equation"> diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20polynomial" title=" Legendre polynomial"> Legendre polynomial</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/125273/operational-matrix-method-for-fuzzy-fractional-reaction-diffusion-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125273.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">201</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">1962</span> A Posteriori Analysis of the Spectral Element Discretization of Heat Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chor%20Nejmeddine">Chor Nejmeddine</a>, <a href="https://publications.waset.org/abstracts/search?q=Ines%20Ben%20Omrane"> Ines Ben Omrane</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Abdelwahed"> Mohamed Abdelwahed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=heat%20equation" title="heat equation">heat equation</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20elements%20discretization" title=" spectral elements discretization"> spectral elements discretization</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20indicators" title=" error indicators"> error indicators</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler" title=" Euler"> Euler</a> </p> <a href="https://publications.waset.org/abstracts/4041/a-posteriori-analysis-of-the-spectral-element-discretization-of-heat-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4041.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">306</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">1961</span> Approximate Solution to Non-Linear Schr枚dinger 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鈥檃 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">1960</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">1959</span> A Mathematical Equation to Calculate Stock Price of Different Growth Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Weiping%20Liu">Weiping Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=stock%20price" title="stock price">stock price</a>, <a href="https://publications.waset.org/abstracts/search?q=multistage%20model" title=" multistage model"> multistage model</a>, <a href="https://publications.waset.org/abstracts/search?q=different%20growth%20model" title=" different growth model"> different growth model</a>, <a href="https://publications.waset.org/abstracts/search?q=discounted%20cash%20flow%20method" title=" discounted cash flow method"> discounted cash flow method</a> </p> <a href="https://publications.waset.org/abstracts/12664/a-mathematical-equation-to-calculate-stock-price-of-different-growth-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12664.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">406</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">1958</span> Energy Conservation and H-Theorem for the Enskog-Vlasov Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Eugene%20Benilov">Eugene Benilov</a>, <a href="https://publications.waset.org/abstracts/search?q=Mikhail%20Benilov"> Mikhail Benilov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Enskog%20collision%20integral" title="Enskog collision integral">Enskog collision integral</a>, <a href="https://publications.waset.org/abstracts/search?q=hard%20spheres" title=" hard spheres"> hard spheres</a>, <a href="https://publications.waset.org/abstracts/search?q=kinetic%20equation" title=" kinetic equation"> kinetic equation</a>, <a href="https://publications.waset.org/abstracts/search?q=phase%20transition" title=" phase transition"> phase transition</a> </p> <a href="https://publications.waset.org/abstracts/97730/energy-conservation-and-h-theorem-for-the-enskog-vlasov-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/97730.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">153</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">1957</span> Numerical Solution of Manning's Equation in Rectangular Channels</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdulrahman%20Abdulrahman">Abdulrahman Abdulrahman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=channel%20design" title="channel design">channel design</a>, <a href="https://publications.waset.org/abstracts/search?q=civil%20engineering" title=" civil engineering"> civil engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=hydraulic%20engineering" title=" hydraulic engineering"> hydraulic engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=open%20channel%20flow" title=" open channel flow"> open channel flow</a>, <a href="https://publications.waset.org/abstracts/search?q=Manning%27s%20equation" title=" Manning's equation"> Manning's equation</a>, <a href="https://publications.waset.org/abstracts/search?q=normal%20depth" title=" normal depth"> normal depth</a>, <a href="https://publications.waset.org/abstracts/search?q=uniform%20flow" title=" uniform flow"> uniform flow</a> </p> <a href="https://publications.waset.org/abstracts/72618/numerical-solution-of-mannings-equation-in-rectangular-channels" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/72618.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">221</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">1956</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">1955</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 Londo帽o </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">1954</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鈥檚 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">1953</span> Analysis of a Generalized Sharma-Tasso-Olver Equation with Variable Coefficients</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fadi%20Awawdeh">Fadi Awawdeh</a>, <a href="https://publications.waset.org/abstracts/search?q=O.%20Alsayyed"> O. Alsayyed</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Al-Shar%C3%A1"> S. Al-Shar谩</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves. <p class="card-text"><strong>Keywords:</strong> <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=multiple%20kink%20solution" title=" multiple kink solution"> multiple kink solution</a>, <a href="https://publications.waset.org/abstracts/search?q=Sharma-Tasso-Olver%20equation" title=" Sharma-Tasso-Olver equation"> Sharma-Tasso-Olver equation</a>, <a href="https://publications.waset.org/abstracts/search?q=inhomogeneity%20of%20media" title=" inhomogeneity of media"> inhomogeneity of media</a> </p> <a href="https://publications.waset.org/abstracts/18827/analysis-of-a-generalized-sharma-tasso-olver-equation-with-variable-coefficients" class="btn btn-primary 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