Application of the -expansion to travelling wave solutions of the Broer–Kaup and the approximate long water wave equations

2008 ◽  
Vol 206 (1) ◽  
pp. 321-326 ◽  
Author(s):  
Mingliang Wang ◽  
Jinliang Zhang ◽  
Xiangzheng Li
Keyword(s):  
Water Wave ◽  
Wave Equations ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

scholarly journals Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities

2018 ◽  
Vol 73 (10) ◽  
pp. 883-892
Author(s):  
Stefan C. Mancas ◽  
Haret C. Rosu ◽  
Maximino Pérez-Maldonado
Keyword(s):  
Dynamical Systems ◽  
Elliptic Equations ◽  
Hypergeometric Functions ◽  
Wave Equations ◽  
Constant Term ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Simple Method ◽  
Solutions Of Wave Equations ◽  
Wave Solutions

AbstractWe use a simple method that leads to the integrals involved in obtaining the travelling-wave solutions of wave equations with one and two exponential nonlinearities. When the constant term in the integrand is zero, implicit solutions in terms of hypergeometric functions are obtained, while when that term is nonzero, all the basic travelling-wave solutions of Liouville, Tzitzéica, and their variants, as as well sine/sinh-Gordon equations with important applications in the phenomenology of nonlinear physics and dynamical systems are found through a detailed study of the corresponding elliptic equations.

Travelling And Periodic Wave Solutions Of Some Nonlinear Wave Equations

2004 ◽  
Vol 59 (7-8) ◽  
pp. 389-396 ◽  
Author(s):  
A. H. Khater ◽  
M. M. Hassan
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Periodic Wave ◽  
Travelling Wave ◽  
Nonlinear Wave Equations ◽  
Travelling Wave Solutions ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Pacs 02.30

We present the mixed dn-sn method for finding periodic wave solutions of some nonlinear wave equations. Introducing an appropriate transformation, we extend this method to a special type of nonlinear equations and construct their solutions, which are not expressible as polynomials in the Jacobi elliptic functions. The obtained solutions include the well known kink-type and bell-type solutions as a limiting cases. Also, some new travelling wave solutions are found. - PACS: 02.30.Jr; 03.40.Kf

New exact travelling wave solutions of bidirectional wave equations

Pramana ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. 819-829 ◽  
Author(s):  
JONU LEE ◽  
RATHINASAMY SAKTHIVEL
Keyword(s):  
Wave Equations ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

Exact Travelling Wave Solutions of the Nonlinear Evolution Equations by Auxiliary Equation Method

2015 ◽  
Vol 70 (11) ◽  
pp. 969-974 ◽  
Author(s):  
Melike Kaplan ◽  
Arzu Akbulut ◽  
Ahmet Bekir
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Equation Method ◽  
Nonlinear Wave Equations ◽  
Auxiliary Equation ◽  
Travelling Wave Solutions ◽  
Auxiliary Equation Method ◽  
Wave Solutions

AbstractThe auxiliary equation method presents wide applicability to handling nonlinear wave equations. In this article, we establish new exact travelling wave solutions of the nonlinear Zoomeron equation, coupled Higgs equation, and equal width wave equation. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions, and rational functions. It is shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering. Throughout the article, all calculations are made with the aid of the Maple packet program.

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