摘要
提出了求非线性数学物理演化方程周期波解的F展开法,该方法可看作最近提出的扩展的Jacobi椭圆函数展开方法的浓缩.直接利用F展开法而不计算Jacobi椭圆函数,我们可同时得到著名的KdV方程的多个用Jacobi椭圆函数表示的周期波解.当模数m→1 时,可得到双曲函数解(包括孤立波解).
We present a F-expansion method for fi nd ing periodic wave solutions of nonlinear evolution equations in mathematical phy sics,which can be thought of as a concentration of extended Jacobi elliptic func tion expansion method proposed more recently.By using the F-expansion,witho ut calculating Jacobi elliptic functions,we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the famous KdV equation.When the modulus m approaches to 1,the hyperbolic function solutio ns (including the solitary wave solutions) are also given.
出处
《应用数学》
CSCD
北大核心
2005年第2期303-307,共5页
Mathematica Applicata
基金
Supported in part by the Natural Science Foundation of Henan Province of China(0111050200)
the Natural Science Foundation of Education Department of Henan Province of China(2003110003)
the Science Foundation of Henan University of Science and Technology(2003QN13)
关键词
F展开法
KDV方程
周期波解
JACOBI椭圆函数
孤立波解
F-expansion
KdV equation
Periodic wave solutions
J acobi elliptic functions
Solitary wave solutions
