求解非线性方程的Jacobi椭圆展开法和F-展式法以KdV方程为例

Solve the nonlinear equation with Jacobi ellicptic function expansion and F-expansion methods illustrated by KdV quation

借助齐次平衡原则,构造一种新的精确解的方法F-展式法。F-展式法可看作最近提出的Jacobi椭圆函数法的推广,获得了KdV方程的多组新的Jacobi椭圆函数解,与其它结果比较,最大的进步是将解表示为两个函数的多项式形式。

By means of the homogeneous balance principle, F-expansion method, a rather new one to construct the precise solutions, is given here. It can be called as the extension of Jacobi elliptic function method. We acquire several new groups of Jacobi elliptic function solutions for KdV equation. Being compared with the results obtained by other methods, its greatest progress is that the solutions can be expressed by a polynomial of two functions.