一类非线性演化方程新的多级准确解

New multi-order exact solutions for nonlinear evolution equations

利用摄动法对NLS方程和Zakharov方程作展开.应用Jacobi椭圆函数展开法求得了零级近似方程的准确解,并在Lamé方程和Lamé函数的基础上分别求得一级近似方程和二级近似方程的准确解.这样,就求得此类非线性演化方程的多级准确解.

The perturbation method is applied to the multi - order exact solutions of nonlinear evolution equations. The exact solutions to the zeroth -order equation can be derived by Jacobi elliptic function expansion method , and then the first - order and the second - order equations can be solved by using Lamé equation and Lamé functions. Thus, the multi - order exact solutions are obtained to the nonlinear evolution equations.