微扰的耦合非线性薛定谔方程的近似求解

将直接微扰方法应用于可积的含修正项的非线性薛定谔方程，通过近似解与精确解的比较确定了直接微扰方法的可靠性.继而，将该方法应用于微扰的耦合非线性薛定谔方程，并获得了该微扰方程的可靠的近似解. 关键词： 直接微扰方法 微扰 耦合非线性薛定谔方程 近似解

Asymptotic solutions of perturbed N-component nonlinear Schr?dinger equations

We apply the direct perturbation method to an integrable nonlinear Schrdinger equation with a correction term to obtain its asymptotic solutions. It is shown that there is a good qualitative agreement between the asymptotic and the exact solutions when ε is small enough. Then the direct perturbation method is applied to the perturbed N-component nonlinear Schrdinger equations and their asymptotical solutions are obtained.