基于Lamé方程和新的Lamé函数,应用摄动方法和Jacobi椭圆函数展开法求解了 立方非线性薛定谔方程, 获得多种新的多级准确解。这些解对应着不同形式的包络周期解。这些解在极限条件下可以退化为各种形式的包络孤波解。 这表明利用Jacobi椭圆函数和Lamé方程,在符号计算的帮助下,可获得若干非线性发展方程的多级渐进周期解。

Based on the Lamé equation and Lamé functions, the perturbation method and Jacobi elliptic function expansion method are applied to construct the multi-order exact solutions to the cubic nonlinear Schr?dinger equation. Some new multi-order envelope periodic solutions are found among the nonlinear evolution equations. These multi-order envelope periodic solutions correspond to different periodic solutions, which can degenerate into the different envelope solitary solutions. It is shown that some multi-order asymptotic periodic solutions to some nonlinear evolution equations in term of Jacobi elliptic functions and Lamé equation are explicitly obtained with the aid of symbolic computation.