用推广的李群约化法求解非线性薛定谔方程

用推广的经典李群约化法，得到了色散系数、非线性系数、补偿（或损失）系数为时、空变量函数时的非线性薛定谔方程的精确解.深入研究了非线性薛定谔模型的一般孤波解与线性调频孤波解在光纤通讯与光纤放大器中的潜在应用. 关键词： 李群约化 非线性薛定谔方程 光纤通讯

Solution of the nonlinear Schr?dinger equation using the generalized Lie group reduction method

In this paper, by using the technique of generalized Lie group reduction, the exact solutions of the nonlinear Schrdinger equation with distributed dispersion, nonlinearity, and gain (or loss) are obtained. And, the potential application of the general solitary wave solutions and the chirped solitary wave solutions in optical fibers communication and optical fibers amplifiers have also been studied thoroughly. This will provide the possibility in making new optical fibers amplifiers.