Lam函数和非线性演化方程的扰动方法

利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函 数展开法求得了零级近似方程的准确解，并由此得到一级近似方程和二级近似方程分别满足 齐次Lam方程和非齐次Lam方程，应用Lam函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样，就求得了非线性演化方程的多级准确解. 关键词： Jacobi椭圆函数 Lam函数 多级准确解 非线性演化方程 扰动方法

LamDe＇ function and perturbation method to nonlinear evolution equations

The perturbation method is applied to the multi-order exact solutions of nonline ar evolution equations. The exact solutions to the zeroth-order equation can be derived by Jacobi elliptic function expansion method, and then the first-order a nd the second-order equations can be rewritten as the homogeneous Lam equa tion and inhomogeneous Lam equation, respectively. They can be solved by using Lam functions and the Jacobi elliptic function expansion method. Thus, the mu lti-order solutions are obtained to the nonlinear evolution equations.