A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

doi:10.1088/1674-1056/19/3/030306

中国物理B ›› 2010, Vol. 19 ›› Issue (3): 30306-030306.doi: 10.1088/1674-1056/19/3/030306

A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

赵银龙, 柳银萍, 李志斌

Department of Computer Science, East China Normal University, Shanghai 200241, China

收稿日期:2009-03-01 修回日期:2009-05-22 出版日期:2010-03-15 发布日期:2010-03-15
基金资助:
Project supported by the National Key Basic Research Project of China (Grant No.~2004CB318000) and the National Natural Science Foundation of China (Grant No.~10771072).

A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

Zhao Yin-Long (赵银龙), Liu Yin-Ping (柳银萍), and Li Zhi-Bin (李志斌)^†

Department of Computer Science, East China Normal University, Shanghai 200241, China

Received:2009-03-01 Revised:2009-05-22 Online:2010-03-15 Published:2010-03-15
Supported by:
Project supported by the National Key Basic Research Project of China (Grant No.~2004CB318000) and the National Natural Science Foundation of China (Grant No.~10771072).

摘要/Abstract

摘要： Recently the (G'/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G'/G)-expansion method is a special form of the truncated Painlevé expansion method by introducing an intermediate expansion method. Then the generalized (G'/G)--(G'/G) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlevé expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the (G'/G)-expansion method.

Abstract: Recently the (G'/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G'/G)-expansion method is a special form of the truncated Painlevé expansion method by introducing an intermediate expansion method. Then the generalized (G'/G)--(G'/G) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlevé expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the (G'/G)-expansion method.

Key words: (G'/G)-expansion method, truncated Painlevé expansion method, mKdV equation, traveling wave solutions

中图分类号: (Solitons)

05.45.Yv

02.30.Jr (Partial differential equations)

赵银龙, 柳银萍, 李志斌. A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation[J]. 中国物理B, 2010, 19(3): 30306-030306.

Zhao Yin-Long (赵银龙), Liu Yin-Ping (柳银萍), and Li Zhi-Bin (李志斌). A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation[J]. Chin. Phys. B, 2010, 19(3): 30306-030306.

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A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

A connection between the (G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

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