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

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

中国物理B ›› 2010, Vol. 19 ›› Issue (8): 80202-080202.doi: 10.1088/1674-1056/19/8/080202

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

刘希忠

Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China

收稿日期:2010-01-04 修回日期:2010-01-13 出版日期:2010-08-15 发布日期:2010-08-15
基金资助:
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).

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

Liu Xi-Zhong(刘希忠)^†

Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2010-01-04 Revised:2010-01-13 Online:2010-08-15 Published:2010-08-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

Key words: approximate homotopy symmetry method, approximate homotopy direct method, generalized Kawahara equation, homotopy series solutions

中图分类号: (Approximations and expansions)

02.30.Mv

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

刘希忠. Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method[J]. 中国物理B, 2010, 19(8): 80202-080202.

Liu Xi-Zhong(刘希忠). Approximate homotopy similarity reduction for the generalized Kawahara equation via Lie symmetry method and direct method[J]. Chin. Phys. B, 2010, 19(8): 80202-080202.

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

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

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