Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation

1987 ◽  
Vol 12 (10) ◽  
pp. 1133-1173 ◽  
Author(s):  
Michael I. Weinstein
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Dynamic Stability ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Long Wave ◽  
Solutions Of Equations

scholarly journals Solitary Wave Solutions of Some Coupled Nonlinear Evolution Equations

2014 ◽  
Vol 6 (2) ◽  
pp. 273-284 ◽  
Author(s):  
K. Khan ◽  
M. A. Akbar
Keyword(s):  
Solitary Wave ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Long Wave

In this article, the modified simple equation (MSE) method has been executed to find the traveling wave solutions of the coupled (1+1)-dimensional Broer-Kaup (BK) equations and the dispersive long wave (DLW) equations. The efficiency of the method for finding exact solutions has been demonstrated. It has been shown that the method is direct, effective and can be used for many other nonlinear evolution equations (NLEEs) in mathematical physics. Moreover, this procedure reduces the large volume of calculations.  Keywords: MSE method; NLEE; BK equations; DLW equations; Solitary wave solutions. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v6i2.16671 J. Sci. Res. 6 (2), 273-284 (2014)  

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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