一类非线性演化方程的多级准确解

The multi-order exact solution for nonlinear evolution equations

利用摄动法对非线性演化方程作展开。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Lam啨方程和Lam啨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庋?就求得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.