利用(G'/G) 展开法求解广义变系数Burgurs方程

J4 ›› 2011, Vol. 28 ›› Issue (6): 674-681.

利用(G'/G) 展开法求解广义变系数Burgurs方程

庞晶,靳玲花,应孝梅

内蒙古工业大学理学院，内蒙古呼和浩特, 010051

收稿日期:2010-11-29 修回日期:2011-01-17 出版日期:2011-11-28 发布日期:2011-11-14
通讯作者: 庞晶(1963-)，博士，教授，研究方向为孤立子与可积系统理论及其应用. E-mail:pang_j@imut.edu.cn
基金资助:
国家教育部博士点基金资助项目(20070128001), 内蒙古自然科学基金资助项目(2010MS0115).

Solving generalized Burgers equation with variable coefficients by (G'/G) -expansion method

PANG Jing, JIN Ling-hua，YING Xiao-mei

College of Science, Inner Mongolia University of Technology, Hohhot 010051, China

Received:2010-11-29 Revised:2011-01-17 Published:2011-11-28 Online:2011-11-14

摘要/Abstract

摘要：

近年来，变系数非线性发展方程受到越来越多的被关注。2008年王明亮等提出了一种新的方法，即(G'/G)展开法。将(G'/G)展开法首次尝试应用到变系数非线性发展方程中，并以广义变系数Burgers方程为例，最终成功得到了在系数满足一定条件时新的精确解；然后又尝试将该展开法进行新的扩展，再一次对广义变系数Burgers方程求解，又成功得到了一些新解。实践证明，该展开法不仅易于求解常系数非线性发展方程，而且对变系数非线性发展方程仍很高效、简洁、实用，并且具有广泛的应用前景。

关键词: 非线性发展方程, 精确解, 广义变系数Burgers方程

Abstract:

In recent years, nonlinear evolution equations with variable coefficients received more and more attention. (G'/G) -expansion method, a new method put forward by Wang Ming-liang et.al in 2008 was applied to the nonlinear evolution equtions with variable coefficients for the first time. The generalized Burgers equation with variable coefficient was taken as an example, and new exact solutions were obtained successfully when the coefficient meets the controlled conditions. Then we try to improve this expansion method, the new solution of generalized Burgers equation with variable coefficients can be obtained successfully once again. It is proved that this expansion method is not only easy when solving nonlinear evolution equations with constant coefficients but also is very efficient, concise and practical when solving the nonlinear evolution equations with variable coefficients, and it also has a broad application.

Key words: nonlinear evolution equations, exact solution, generalized Burgers equation with variable coefficient

中图分类号:

O175.29

庞晶靳玲花应孝梅. 利用(G'/G) 展开法求解广义变系数Burgurs方程[J]. J4, 2011, 28(6): 674-681.

PANG Jing, JIN Ling-hua，YING Xiao-mei. Solving generalized Burgers equation with variable coefficients by (G'/G) -expansion method[J]. J4, 2011, 28(6): 674-681.

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