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

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 meshl...

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Bibliographic Details
Published in:Mathematics (Basel) Vol. 8; no. 9; p. 1601
Main Authors: Avazzadeh, Zakieh, Nikan, Omid, Machado, José A. Tenreiro
Format: Journal Article
Language:English
Published: MDPI AG 01-09-2020
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8091601