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

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.

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

Received: 01 March 2009
Revised: 22 May 2009
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	02.30.Jr	(Partial differential equations)

Fund: 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).

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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 2010 Chin. Phys. B 19 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

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