一类推广的[G′/G]展开方法及其在非线性数学物理方程中的应用

J4 ›› 2010, Vol. 45 ›› Issue (4): 100-105.

一类推广的[G′/G]展开方法及其在非线性数学物理方程中的应用

吕海玲,刘希强,牛磊

聊城大学数学科学学院, 山东聊城 252059

收稿日期:2009-06-07 出版日期:2010-04-10 发布日期:2010-05-19

A generalized [G′/G]expansion method and its applications in nonlinear mathematical physics equations

LV Hai-Ling, LIU Xi-Qiang, NIU Lei

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, Shandong, China

Received:2009-06-07 Online:2010-04-10 Published:2010-05-19
About author:Lv Hai-ling(1983-),female,postgraduate,major in the exact solutions of nonlinear evolution equations.Email:lvhailing20090908@126.com
Supported by:
Supported by the Natural Science Foundation of Shandong Province in China (Y 2008A 35 and Y 2007G 64)

摘要/Abstract

摘要：

研究王明亮的[G′/G]展开方法和一个含有六阶非线性项的一阶常微分方程, 提出一类推广的[G′/G]展开方法。显然, 这个方法可以应用到(2+1)维色散长波方程和双sine-Gordon方程，得到一些新的精确行波解, 包括孤波解, 三角周期波解, 双曲解, 有理解和雅可比椭圆双周期波解。这种方法也可以应用到其他的非线性发展方程中。

关键词: 推广的[G′/G\展开方法;色散长波方程;双sine-Gordon方程;行波解

Abstract:

A generalized [G′/G]-expansion method is proposed by studying Wang′s [G′/G]-expansionmethod and the first order nonlinear ordinary differential equation with a sixth-order nonlinear term. The method is applied to (2+1)-dimensional dispersive long wave equations and double sineGordon equation. As a result, some new exact travelling wave solutions are obtained which include solitary wave solutions, triangular periodic wave solutions, hyperbolic solutions, rational solutions and Jacobi elliptic doubly periodic wave solutions. This method can also be applied to other nonlinear evolution equations in mathematical physics.

Key words: generalized[ G′/G]expansion method; dispersive long wave equations; double sine-Gordon equation; travelling wave solution

吕海玲,刘希强,牛磊. 一类推广的[G′/G]展开方法及其在非线性数学物理方程中的应用[J]. J4, 2010, 45(4): 100-105.

LV Hai-Ling, LIU Xi-Qiang, NIU Lei. A generalized [G′/G]expansion method and its applications in nonlinear mathematical physics equations[J]. J4, 2010, 45(4): 100-105.

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