scholarly journals Stable and Unstable Solitary-Wave Solutions of the Generalized Regularized Long-Wave Equation

2000 ◽  
Vol 10 (6) ◽  
pp. 603-638 ◽  
Author(s):  
J. L. Bona ◽  
W. R. McKinney ◽  
J. M. Restrepo
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Long Wave ◽  
Regularized Long Wave Equation

scholarly journals On the wave solutions to the TRLW equation

2018 ◽  
Vol 22 ◽  
pp. 01033
Author(s):  
Tukur Abdulkadir Sulaiman ◽  
Canan Unlu ◽  
Hasan Bulut
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Nonlinear Models ◽  
Soliton Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
2D And 3D ◽  
Singular Soliton

In this study, a nonlinear model is investigated, namely; the time regularized long wave equation. Various solitary wave solutions are constructed such as the non-topological, compound topological-non-topological bell-type, singular and compound singular soliton solutions. Under the choice of suitable parameters values, the 2D and 3D graphs to all the obtained solutions are plotted. The reported results in this study may be helpful in explaining the physical meanings of some important nonlinear models arising in the field of nonlinear science.

scholarly journals Traveling solitary wave solutions for the symmetric regularized long-wave equation

2015 ◽  
Vol 11 (8) ◽  
pp. 5520-5528
Author(s):  
Mostafa Khater ◽  
Mahmoud AE Abdelrahman
Keyword(s):  
Wave Equation ◽  
Solitary Wave ◽  
Traveling Wave ◽  
Function Method ◽  
Traveling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions ◽  
Long Wave ◽  
Regularized Long Wave Equation

In this paper, we employ the extended tanh function method to nd the exact traveling wave solutions involving parameters of the symmetric regularized long- wave equation. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. These studies reveal that the symmetric regularized long-wave equation has a rich varietyof solutions.

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

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1601
Author(s):  
Zakieh Avazzadeh ◽  
Omid Nikan ◽  
José A. Tenreiro Machado
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Solitary Wave ◽  
Wave Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Ode System ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
De Vries

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.

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