Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method

doi:10.1088/1674-1056/19/8/080202

Abstract This paper studies the generalized Kawahara equation in terms of the approximate homotopy symmetry method and the approximate homotopy direct method. Using both methods it obtains the similarity reduction solutions and similarity reduction equations of different orders, showing that the approximate homotopy direct method yields more general approximate similarity reductions than the approximate homotopy symmetry method. The homotopy series solutions to the generalized Kawahara equation are consequently derived.

Keywords: approximate homotopy symmetry method approximate homotopy direct method generalized Kawahara equation homotopy series solutions

Received: 04 January 2010
Revised: 13 January 2010
Accepted manuscript online:

PACS:	02.30.Mv	(Approximations and expansions)
	02.20.Hj	(Classical groups)
	02.20.Qs	(General properties, structure, and representation of Lie groups)
	02.30.Jr	(Partial differential equations)

Fund: Project supported by the National Natural Science Foundations of China (Grant Nos. 10735030, 10475055, 10675065 and 90503006), the National Basic Research Program of China (Grant No. 2007CB814800).

Cite this article:

Liu Xi-Zhong(刘希忠) Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method 2010 Chin. Phys. B 19 080202

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Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method

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