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

作　　者：刘希忠 

机构地区：[1]Department of Physics,Shanghai Jiao Tong University

出　　处：《Chinese Physics B》2010年第8期28-34,共7页中国物理B（英文版）

基　　金：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：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.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.

关 键 词：approximate homotopy symmetry method approximate homotopy direct method generalized Kawahara equation homotopy series solutions 

分 类 号：O175[理学—数学]