A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

2009 ◽  
Vol 42 (2) ◽  
pp. 911-915 ◽  
Author(s):  
Huiqun Zhang
Keyword(s):  
Nonlinear Equations ◽  
Travelling Wave ◽  
Equation Method ◽  
Travelling Wave Solutions ◽  
Wave Solutions

scholarly journals A simple and direct method for generating travelling wave solutions for nonlinear equations

2008 ◽  
Vol 323 (5) ◽  
pp. 1150-1167 ◽  
Author(s):  
D. Bazeia ◽  
Ashok Das ◽  
L. Losano ◽  
A. Silva
Keyword(s):  
Nonlinear Equations ◽  
Direct Method ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

New Non-Travelling Wave Solutions of Calogero Equation

2016 ◽  
Vol 8 (6) ◽  
pp. 1036-1049 ◽  
Author(s):  
Xiaoming Peng ◽  
Yadong Shang ◽  
Xiaoxiao Zheng
Keyword(s):  
Nonlinear Equations ◽  
Symbolic Computation ◽  
Travelling Wave ◽  
Explicit Solutions ◽  
Travelling Wave Solutions ◽  
Variable Separation ◽  
Test Technique ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Variable Separation Approach

AbstractIn this paper, the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation. The equation is reduced to some (1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test technique. Based on this idea and with the aid of symbolic computation, some new explicit solutions can be obtained.

Three Kind of Triangle Rational Functions and Applications for Discrete Nonlinear Equations

2011 ◽  
Vol 317-319 ◽  
pp. 2168-2171
Author(s):  
Xiu Rong Guo ◽  
Zheng Tao Liu ◽  
Mei Guo
Keyword(s):  
Nonlinear Equations ◽  
Difference Equations ◽  
Soliton Solutions ◽  
Rational Functions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Periodic Travelling Wave ◽  
Formal Solutions

In order to efficiently search for new soliton solutions to differential-difference equations (DDEs), three kinds of triangle rational functions are first introduced. Then a kind of formal solutions of DDEs are presented which are expressed by a unified nonlinear combination of the three kinds of triangle rational functions. As illustrative examples, the periodic travelling-wave solutions of the discrete modified KdV(mKdV) equations are obtained.

Analytic bounded travelling wave solutions of some nonlinear equations II

2009 ◽  
Vol 41 (2) ◽  
pp. 803-810
Author(s):  
Eugenia N. Petropoulou ◽  
Panayiotis D. Siafarikas ◽  
Ioannis D. Stabolas
Keyword(s):  
Nonlinear 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.

Generalized tanh Method Extended to Special Types of Nonlinear Equations

2002 ◽  
Vol 57 (8) ◽  
pp. 692-700 ◽  
Author(s):  
Engui Fan ◽  
Y. C. Hona
Keyword(s):  
Nonlinear Equations ◽  
Gordon Equation ◽  
Kdv Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Sine Gordon Equation ◽  
Wave Solutions ◽  
Tanh Method

By some ‘pre-possessing’ techniques we extend the generalized tanh method to special types of nonlinear equations for constructing their multiple travelling wave solutions. The efficiency of the method can be demonstrated for a large variety of special equations such as those considered in this paper, double sine-Gordon equation, (2+1)-dimensional sine-Gordon equation, Dodd-Bullough- Mikhailov equation, coupled Schrödinger-KdV equation and (2+1)-dimensional coupled Davey- Stewartson equation. - Pacs: 03.40.Kf; 02.30.Jr.

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