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

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.

The periodic wave solutions for two systems of nonlinear wave equations

2003 ◽  
Vol 12 (12) ◽  
pp. 1341-1348 ◽  
Author(s):  
Wang Ming-Liang ◽  
Wang Yue-Ming ◽  
Zhang Jin-Liang
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Periodic Wave ◽  
Nonlinear Wave Equations ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Two Systems

Classification of all travelling-wave solutions for some nonlinear dispersive equations

2007 ◽  
Vol 365 (1858) ◽  
pp. 2291-2298 ◽  
Author(s):  
Jonatan Lenells
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Travelling Wave ◽  
Nonlinear Wave Equations ◽  
Dispersive Equations ◽  
Travelling Wave Solutions ◽  
Nonlinear Dispersive Equations ◽  
Wave Solutions ◽  
Wave Profiles

We present a method for the classification of all weak travelling-wave solutions for some dispersive nonlinear wave equations. When applied to the Camassa–Holm or the Degasperis–Procesi equation, the approach shows the existence of not only smooth, peaked and cusped travelling-wave solutions, but also more exotic solutions with fractal-like wave profiles.

scholarly journals Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Lijun Zhang ◽  
Chaudry Masood Khalique
Keyword(s):  
Solitary Wave ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Kdv Equation ◽  
Periodic Wave ◽  
Sixth Order ◽  
Nonlinear Wave Equations ◽  
Lax Equation ◽  
Periodic Wave Solutions ◽  
Wave Solutions

We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.

BIFURCATIONS OF TRAVELING WAVE SOLUTIONS FOR FOUR CLASSES OF NONLINEAR WAVE EQUATIONS

2005 ◽  
Vol 15 (12) ◽  
pp. 3973-3998 ◽  
Author(s):  
JIBIN LI ◽  
GUANRONG CHEN
Keyword(s):  
Solitary Wave ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Nonlinear Wave Equations ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Kink Wave

Four large classes of nonlinear wave equations are studied, and the existence of solitary wave, kink and anti-kink wave, and uncountably many periodic wave solutions is proved. The analysis is based on the bifurcation theory of dynamical systems. Under some parametric conditions, various sufficient conditions for the existence of the aforementioned wave solutions are derived. Moreover, all possible exact parametric representations of solitary wave, kink and anti-kink wave, and periodic wave solutions are obtained and classified.

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