修正的F展开法和推广的KdV方程新的孤波解和精确解

The extended F-expansion method and new exact solutions of the generalized KdV equation

对F展开法进行了修正,附加含任意常数的负指数项,解决了精确解的奇点问题.用此方法讨论推广的KdV方程的周期波解.在特别情形下,获得了新的Jacobi椭圆函数精确解、孤波解和三角函数解.

In this paper,the F-expansion method is revised by adding a term with negative index with constant c,then the irregular wave solutions are avoided.By using this method,different new periodic wave solutions expressed by the generalized KdV equation are obtained.In the special cases,these periodic wave solutions degenerate to the corresponding Jacobi elliptic function solutions,solitary wave solutions or trigonometric function solutions.