Jacobi elliptic function expansion method under a general function transform and its applications
一般变换下的Jacobi椭圆函数展开法及应用

A Jacobi elliptic function expansion method under a general function transform, which is more general than the Jacobi elliptic function expansion method under a traveling wave transform, is proposed to construct the exact solutions of nonlinear evolution equations. It is shown that some new exact periodic solutions of them are obtained by this method and these new solutions include previous solutions. Meanwhile, it is proved that the periodic solutions of some nonlinear evolution equations must be traveling solutions.