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travelling wave solutions to the m-KdV-Sine-Gordon Equation and the m-KdV-Sinh-Gordon Equation

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Chinese Quarterly Journal of Mathematics 2013年第1期28卷 82-86页

作者： LI Er-qiang CHEN Jin-lan School of Mathematics and Statistics Henan University of Science and Technology Luoyang 471003China

By using the function transformation and proper Sub-ODE, exact travelling wave solutions of the m-KdV-Sine-Gordon and the m-KdV-Sinh-Gordon equation are obtained, from which exact travelling wave solutions of the m-Kd... 详细信息

关键词： function transformation m-KdV-Sine-Gordon equation m-KdV-Sinh-Gordon equation Sub-ODE travelling wave solutions

travelling wave solutions for Generalized KdV-mKdV Equation

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Journal of Southwest Jiaotong University(English Edition) 2009年第4期17卷 366-369页

作者：秦亚赖绍永 College of Mathematics and Information Science Neijiang Normal University College of Mathematics and Software Science Sichuan Normal University Department of Economic Mathematics Southwestern University of Finance and Economics

A technique based on reduction of order for solving ordinary differential equations is developed to find exact solutions for a generalized KdV-mKdV equation that possesses high order nonlinear terms. The analytical expressions of several types of traveUing wave solutions for the equation are obtained in terms of sin, cos, tan, cot, sinh, cosh, tanh, coth and algebraic profiles. It is shown that the wave speed of travelling wave solutions and the coefficient of low order derivative term in the equation are two main factors to determine the change in the physical structures of solutions.

关键词： Generalized Kd V-mKd V equations Order-reduction technique travelling wave solutions Periodic solutions Explicit expressions

On New travelling wave solutions of the Generalized K-S Equation

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Journal of Shanghai University(English Edition) 2002年第4期6卷 288-291页

作者：彭国俊李常品 Department of Mathematics College of Sciences Shanghai University Shanghai China

The new analytical travelling wave solutions to the generalized Kuramoto Sivashinsky (K S) equation were obtained by introducing a special transformation.

关键词： travelling wave solutions solitary wave solutions Kuramoto Sivashinsky equation.

The properties of travelling wave solutions for Kdv-Burgers-Kuramoto equation 25th

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The properties of travelling wave solutions for Kdv-Burgers-...

Exact travelling wave solutions for a Combined KdV and Schwarzian KdV Equation

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作者： Hu Yanxia School of Mathematics and Physics North China Electric Power University

ISBN: (纸本)9781467355339

The travelling wave solutions for Kdv-Burgers-Kuramoto equation are considered. The nonexistence of firs integrals of traveling wave solutions equation of Kdv-Burgers-Kuramoto equation is shown. Therefore, a sufficien condition of nonexistence of travelling wave solutions of Kdv-Burgers-Kuramoto equation is given. Two independent one-parameter Lie groups admitted by travelling wave solutions equation of Kdv-Burgers-Kuramoto equation are obtained.

关键词： Nonexistence travelling wave solutions First integral Lie group Kdv-Burgers-Kuramoto equation

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Chinese Quarterly Journal of Mathematics 2012年第3期27卷 371-374页

作者： LI Ling-xiao LI Er-qiang College of Mathematics and Statistics Henan University of Science and Technology Luoyang 471003China

In this paper the ( G'/G )-expansion method is used to find exact travelling wave solutions for a combined KdV and Schwarzian KdV equation. As a result, multiple travelling wave solutions with arbitrary parameters are obtained, which are expressed by hyperbolic functions, trigonometric functions and rational functions. When the parameters are taken as special values, the solitary waves are derived from the travelling waves. The (G'/G)-expansion method presents a wider applicability for handling nonlinear wave equations.

关键词： the (G’/G)-expansion method travelling wave solutions homogeneous balance the combined KdV and Schwarzian KdV equation

EXACT travelling wave solutions TO BBM EQUATION

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Annals of Differential Equations 2009年第4期25卷 414-419页

作者： Zhu Li, Jingen Yang (College of Math. and Information Science, Xinyang Normal University, Xinyang 464000, Henan) Jirong Shan (Education Bureau of Sishui, Sishui 273200, Shandong)

Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.

关键词： nonlinear evolution equation Jacobian elliptic function travelling wave solutions

travelling solitary wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order

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Chinese Physics B 2009年第8期18卷 3169-3173页

作者：邓习军燕子宗韩立波 School of Information and Mathematics Yangtze University College of Physical Science and Technology Yangtze University

In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.

关键词： travelling wave solutions first integral method generalized Burgers-Huxley equation with nonlinear terms of any order

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一类反应扩散方程的行波解

高等学校计算数学学报 2000年第2期22卷 175-182页

作者：周轩伟温州大学数学系!温州325027

In this paper we discuss travelling wave solutions to a class of reaction diffusion equations containing a convection term. The existence and approximation results of the solutions are established and the error estima... 详细信息

关键词： Convection Term Reaction Diffusion Equations travelling wave solutions Error Estimates.

Singular solitons and other solutions to a couple of nonlinear wave equations

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Chinese Physics B 2013年第6期22卷 115-121页

作者： Mustafa Inc Esma Ulutas Anjan Biswas Firat University Department of Mathematics23119 ElazgTürkiye Bitlis Eren University Deparment of StatisticBitlis Türkiye Department of Mathematical Sciences Delaware State UniversityDover DE 19901-2277 USA

This paper addresses the extended （G′/G）-expansion method and applies it to a couple of nonlinear wave equations. These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation. This extended method reveals several solutions to these equations. Additionally, the singular soliton solutions are revealed, for these two equations, with the aid of the ansatz method.

关键词： (G′/G)-expansion method travelling wave solutions singular soliton mBBM and Boussinesqequations