ON THE GENERALIZED TANH METHOD FOR THE (2+1)-DIMENSIONAL BREAKING SOLITON EQUATION

1995 ◽  
Vol 10 (38) ◽  
pp. 2937-2941 ◽  
Author(s):  
BO TIAN ◽  
YI-TIAN GAO
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
The Self ◽  
Solitary Wave Solutions ◽  
Soliton Equation ◽  
Yang Mills ◽  
Wave Solutions ◽  
Tanh Method ◽  
Open Question

There is an open question as to whether or not the recently-proposed tanh method can be modified in order to proceed beyond the traveling or solitary wave solutions for nonlinear evolution equations. On the other hand, the class of the breaking soliton equations, which the self-dual Yang-Mills equation is found to belong to, is of current interest. In this letter, we propose a generalized tanh method, with symbolic computation, to construct a family of soliton-like solutions for a (2+1)-dimensional breaking soliton equation.

scholarly journals Multiple Exact Travelling Solitary Wave Solutions of Nonlinear Evolution Equations

2019 ◽  
pp. 1-13
Author(s):  
M. M. El-Horbaty ◽  
F. M. Ahmed
Keyword(s):  
Riccati Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Extended Form ◽  
Wave Solutions ◽  
Tanh Method

An extended Tanh-function method with Riccati equation is presented for constructing multiple exact travelling wave solutions of some nonlinear evolution equations which are particular cases of a generalized equation. The results of solitary waves are general compact forms with non-zero constants of integration. Taking the full advantage of the Riccati equation improves the applicability and reliability of the Tanh method with its extended form.

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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