New Exact Travelling Wave Solutions for Generalized Zakharov–Kuzentsov Equations Using General Projective Riccati Equation Method

2004 ◽  
Vol 41 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Chen Yong ◽  
Li Biao
Keyword(s):  
Riccati Equation ◽  
Travelling Wave ◽  
Equation Method ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Projective Riccati Equation Method

scholarly journals Abundant Exact Solition-Like Solutions to the Generalized Bretherton Equation with Arbitrary Constants

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xiuqing Yu ◽  
Fengsheng Xu ◽  
Lihua Zhang
Keyword(s):  
Full Advantage ◽  
Riccati Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

The Riccati equation is employed to construct exact travelling wave solutions to the generalized Bretherton equation. Taking full advantage of the Riccati equation which has more new solutions, abundant new multiple solition-like solutions are obtained for the generalized Bretherton equation.

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.

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.

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