阻尼非线性Schrdinger方程的数值研究及其在光孤立子通信中的应用

Numerical Study on the Damped Nonlinear Schrbdinger Equation with Applications to Optical Soliton Communication

本文用Petrov-Galerkin有限元法构造了求解阻尼非线性Schr(?)dinger方程初值问题高精度的通用数值格式。使用此格式,先在无阻尼的情况下数值求解了单个和多个、一阶和高阶孤立子的传播及相互作用问题。所得数值解与分析解高度吻合,从而考验了本方法的精度和稳定性。然后加上阻尼项,得到阻尼使一阶和高阶孤立子在传播和相互作用中振幅衰减和周期延长的具体规律,从而为光孤立子通信总体方案设计和参数选择提供了一个有效的数值实验手段。

A numerical scheme for solving the damped nonlinear Schrodinger equation is constructed by a Petrov-Galerkin finite element method. The comparison of the numerical and exact solutions of the single soliton , multiple and high order solitons shows the excellent accuracy and stability of the scheme. The other numerical solutions explain the theory of the optical soliton and its applications to the optical soliton communication quite well, so this scheme provides an useful numerical method in designing optical soliton communication systems.