The extended auxiliary the KdV equation with equation method for variable coefficients  

作　　者：Shi Lan-Fang Chen Cai-Sheng Zhou Xian-Chun 

机构地区：[1]College of Mathematics, Hohai University, Nanjing 210098, China [2]College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China [3]College of Electronic and Information Engineering,Nanjing University of Information Science and Technology, Nanjing 210044, Chins

出　　处：《Chinese Physics B》2011年第10期166-170,共5页中国物理B（英文版）

基　　金：Project supported by the Fundamental Research Funds for the Central Universities （Grant No. 2010B17914） and the National Natural Science Foundation of China （Grant No. 10926162）.

摘　　要：This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.

关 键 词：extended auxiliary equation method KdV equation with variable coefficients exactsolutions 

分 类 号：O175.29[理学—数学] O415[理学—基础数学]