含三阶色散项的非线性薛定谔方程的微扰对称和近似解

The approximate symmetry perturbation and approximate solutions of the nonlinear Schrdinger equations with the term of third order group velocity dispersion

利用微扰对称方法和经典李群方法的结合,研究了含三阶群速度色散(GVD)的非线性薛定谔方程,得到了该方程关于高阶微扰的近似解和约化常微分方程.并考虑了不同情况下的有限阶微扰项或无穷阶微扰的相似解和约化常微分方程.

The approximate symmetry perturbation plied to study nonlinear Schroedinger equation with method combining with classical Lie group method was apthird order group velocity dispersion （ GVD ）. Similarity solutions and reduction ordinary differential equation were obtained for the corresponding high order modifications. Similarity solutions and reduction equations corresponding finite and infinite order modifications were als considered under different conditions.