用F展开法解变系数KdV方程  

Solving KdV equation with variable coefficients by using F-expansion method

作　　者：李向正[1] 张金良[1] 王明亮[1] 

机构地区：[1]河南科技大学理学院,河南洛阳471003

出　　处：《云南大学学报（自然科学版）》2006年第3期222-226,共5页Journal of Yunnan University(Natural Sciences Edition)

基　　金：河南省自然科学基金资助项目(0111050200);河南科技大学科学研究基金资助项目(2004ZD002和2006ZY001)

摘　　要：扩展了最近提出的F展开方法以构造变系数非线性演化方程更多的精确解,即将F展式中的常系数代之以变系数.作为例子,用扩展的F展开法解变系数KdV方程,得到了很丰富的精确解,特别是以2个不同的Jacobi椭圆函数表示的解.显然扩展的F展开方法也可以解其他类型的变系数非线性演化方程.F-expansion method proposed recently is extended to construct more exact solutions of nonlinear evolution equations with variable coefficients. To be more precise, variable coefficients is used instead of constant coefficients in F-expansion. As an illustrative example, by using the extended F-expansion method KdV equation with variable coefficients is solved, an abundance of exact solutions, especially the solutions expressed by two different Jacobi elliptic functions, have been obtained. Obviously, the extended F-expansion method can be applied to solve other type of nonlinear evolution equations with variable coefficients as well.

关 键 词：F展开法 变系数KDV方程 JACOBI椭圆函数 精确解 

分 类 号：O175.2[理学—数学]