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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MDPI AG
2020-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/9/1601 |
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| author | Zakieh Avazzadeh Omid Nikan José A. Tenreiro Machado |
| author_facet | Zakieh Avazzadeh Omid Nikan José A. Tenreiro Machado |
| author_sort | Zakieh Avazzadeh |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T16:16:33Z |
| format | Article |
| id | doaj.art-cc92533ef7d74d618adb996967703308 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T16:16:33Z |
| publishDate | 2020-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cc92533ef7d74d618adb9969677033082023-11-20T14:02:50ZengMDPI AGMathematics2227-73902020-09-0189160110.3390/math8091601Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW EquationZakieh Avazzadeh0Omid Nikan1José A. Tenreiro Machado2Institute of Research and Development, Duy Tan University, Da Nang 550000, VietnamSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, IranDepartment of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, 4249-015 Porto, PortugalThis 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.https://www.mdpi.com/2227-7390/8/9/1601nonlinear wave phenomenRBFlocal RBF-FDstability |
| spellingShingle | Zakieh Avazzadeh Omid Nikan José A. Tenreiro Machado Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation Mathematics nonlinear wave phenomen RBF local RBF-FD stability |
| title | Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation |
| title_full | Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation |
| title_fullStr | Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation |
| title_full_unstemmed | Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation |
| title_short | Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation |
| title_sort | solitary wave solutions of the generalized rosenau kdv rlw equation |
| topic | nonlinear wave phenomen RBF local RBF-FD stability |
| url | https://www.mdpi.com/2227-7390/8/9/1601 |
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