A series of abundant exact travelling wave solutions for a modified generalized Vakhnenko equation using auxiliary equation method

2009 ◽  
Vol 211 (1) ◽  
pp. 102-107 ◽  
Author(s):  
Yulan Ma ◽  
Bangqing Li ◽  
Cong Wang
Keyword(s):  
Travelling Wave ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Travelling Wave Solutions ◽  
Auxiliary Equation Method ◽  
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.

AUXILIARY EQUATION METHOD AND ITS APPLICATIONS TO NONLINEAR EVOLUTION EQUATIONS

2003 ◽  
Vol 14 (08) ◽  
pp. 1075-1085
Author(s):  
SIRENDAOREJI ◽  
SUN JIONG
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Partial Differential Equations ◽  
Algebraic Method ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Auxiliary Equation ◽  
Travelling Wave Solutions ◽  
Auxiliary Equation Method ◽  
Wave Solutions

By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.

scholarly journals Extended Auxiliary Equation Method to the perturbed Gerdjikov-Ivanov Equation

2018 ◽  
Author(s):  
Jamilu Sabi'u ◽  
Hadi Rezazadeh ◽  
Mostafa Eslami ◽  
Alper Korkmaz
Keyword(s):  
Travelling Wave ◽  
Equation Method ◽  
Auxiliary Equation ◽  
Travelling Wave Solutions ◽  
Linear Optics ◽  
Extended Form ◽  
Auxiliary Equation Method ◽  
First Order ◽  
Non Linear Optics ◽  
New Form

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

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