广义变系数(3+1)-维非线性薛定谔方程的有限对称群解

基于推广的对称群方法和符号计算，研究了变系数非线性薛定谔方程的有限对称群解。 我们构造了标准的(3+1)-维非线性薛定谔方程和带色散项、非线性项和增益或损耗项的(3+1)-维非线性薛定谔方程的对称变换。 利用该变换，我们从标准的(3+1)-维非线性薛定谔方程中得到了(3+1)-维变系数非线性薛定谔方程丰富的精确解。

Finite symmetry group solutions to generalized variable coefficient (3+1)-D nonlinear Schr(o)dinger equation

In this paper, on the basis of the extending symmetry group approach and symbolic computation, some finite symmetry group solutions of the nonlinear Schr\"{o}dinger (NLS) equations with various variable coefficients are investigated. We construct some symmetry transformations between the standard (3+1)-dimensional NLS equation and (3+1)-dimensional NLS equations with distributed dispersion,nonlinearity and gain or loss. By using these symmetry transformations, rich exact solutions of some (3+1)-dimensional variable coefficients NLS equations are obtained from the standard (3+1)-dimensional NLS equation.