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Open AccessArticle

Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation

Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Vietnam
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran
Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, 4249-015 Porto, Portugal
Author to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1601;
Received: 21 August 2020 / Revised: 9 September 2020 / Accepted: 9 September 2020 / Published: 17 September 2020
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau–Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of the equation is approximated by a local meshless technique called radial basis function (RBF) and the finite-difference (FD) method. The association of the two techniques leads to a meshless algorithm that does not requires the linearization of the nonlinear terms. First, the partial differential equation is transformed into a system of ordinary differential equations (ODEs) using radial kernels. Then, the ODE system is solved by means of an ODE solver of higher-order. It is shown that the proposed method is stable. In order to illustrate the validity and the efficiency of the technique, five problems are tested and the results compared with those provided by other schemes. View Full-Text
Keywords: nonlinear wave phenomen; RBF; local RBF-FD; stability nonlinear wave phenomen; RBF; local RBF-FD; stability
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Avazzadeh, Z.; Nikan, O.; Machado, J.A.T. Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation. Mathematics 2020, 8, 1601.

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