Approximate homotopy symmetry method:Homotopy series solutions to the sixth-order Boussinesq equation  

作　　者：JIAO XiaoYu1,GAO Yuan1 & LOU SenYue1,2,3 1 Department of Physics,Shanghai Jiao Tong University,Shanghai 200240,China 2 Department of Physics,Ningbo University,Ningbo 315211,China 3 School of Mathematics,Fudan University,Shanghai 200433,China 

出　　处：《Science China(Physics,Mechanics & Astronomy)》2009年第8期1169-1178,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant Nos. 10735030, 10475055, 10675065, and 90503006);the National Basic Research Pro-gram of China (Grant No. 2007CB814800);the Program for Changjiang Scholars and Innovative Research Team (Grant No. IRT0734);the Research Fund of Postdoctoral of China (Grant No. 20070410727);the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20070248120) Recommended by LIAO ShiJun

摘　　要：An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation,which arises from fluid dynamics.We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders,educing the related homotopy series solutions.Zero-order similarity reduction equations are equivalent to the Painlevé IV type equation or Weierstrass elliptic equation.Higher order similarity solutions can be obtained by solving linear variable coefficients ordinary differential equations.The auxiliary parameter has an effect on the convergence of homotopy series solutions.Series solutions and similarity reduction equations from the approximate symmetry method can be retrieved from the approximate homotopy symmetry method.An approximate homotopy symmetry method for nonlinear problems is proposed and applied to the sixth-order Boussinesq equation, which arises from fluid dynamics. We summarize the general formulas for similarity reduction solutions and similarity reduction equations of different orders, educing the related homotopy series solutions. Zero-order similarity reduction equations are equivalent to the Painlevé IV type equation or Weierstrass elliptic equation. Higher order similarity solutions can be obtained by solving linear variable coefficients ordinary differential equations. The auxiliary parameter has an effect on the convergence of homotopy series solutions. Series solutions and similarity reduction equations from the approximate symmetry method can be retrieved from the approximate homotopy symmetry method.

关 键 词：APPROXIMATE HOMOTOPY SYMMETRY method sixth-order BOUSSINESQ EQUATION HOMOTOPY series solutions 

分 类 号：O175[理学—数学]