中文摘要：

基于推广的对称群方法和符号计算,一些变系数非线性薛定谔方程的有限对称群解得到了研究.在推广对称群的基础上,对超定方程组分3种情况讨论,构造6种对称变换,并推导出标准的（3＋1）-维非线性薛定谔方程和（3＋1）-维变系数非线性薛定谔方程之间的关系.利用对称变换,从标准的（3＋1）-维非线性薛定谔方程解中得到了（3＋1）-维变系数非线性薛定谔方程丰富的精确解。

英文摘要：

Based on the extending symmetry group approach and symbolic computation,some finite symmetry group solutions of the nonlinear Schrodinger（NLS）equations with various variable coefficients are investigated.On the basis of the extending symmetry group,determining equations are discussed in three kinds of cases,then six kinds of symmetry transformations are constructed and the relations between the standard（3＋1）-D NLS equation and（3＋1）-D variable coefficient NLS equations are derived.By using these symmetry transformations,rich exact solutions of some（3＋1）-D variable coefficient NLS equations are obtained from the standard（3＋1）-D NLS equation.