Construction of the numerical and analytical wave solutions of the Joseph–Egri dynamical equation for the long waves in nonlinear dispersive systems

2020 ◽  
Vol 34 (30) ◽  
pp. 2050289
Author(s):  
Abdulghani R. Alharbi ◽  
M. B. Almatrafi ◽  
Aly R. Seadawy
Keyword(s):  
Solitary Wave ◽  
Numerical Solution ◽  
Evolution Equations ◽  
Dynamical Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Stability

The Kudryashov technique is employed to extract several classes of solitary wave solutions for the Joseph–Egri equation. The stability of the achieved solutions is tested. The numerical solution of this equation is also investigated. We also present the accuracy and the stability of the numerical schemes. Some two- and three-dimensional figures are shown to present the solutions on some specific domains. The used methods are found useful to be applied on other nonlinear evolution 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)  

Auto-Bäcklund Transformation and Solitary-wave Solutions to Non- integrable Generalized Fifth-order Nonlinear Evolution Equations

1999 ◽  
Vol 54 (8-9) ◽  
pp. 549-553 ◽  
Author(s):  
Woo-Pyo Hong ◽  
Young-Dae Jung
Keyword(s):  
Solitary Wave ◽  
Symbolic Computation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
New Class ◽  
Wave Solutions ◽  
Fifth Order ◽  
Truncated Painlevé Expansion

We show that the application of the truncated Painlevé expansion and symbolic computation leads to a new class of analytical solitary-wave solutions to the general fifth-order nonlinear evolution equations which include Lax, Sawada-Kotera (SK), Kaup-Kupershmidt (KK), and Ito equations. Some explicit solitary-wave solutions are presented.

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