标题： 高阶对称性对于线性和非线性薛定谔方程 显示英文标题

标题： Higher order symmetries for linear and nonlinear Schroedinger equations

摘要： 我们研究了具有任意空间变量数目的线性薛定谔方程的任意阶对称算子。 我们推导出此类算子系数函数的决定方程，并详细考虑了一些这些方程可以显式求解的情形。 此外，还给出了非线性薛定谔方程的完全群分类。 显示英文摘要

摘要： We study arbitrary order symmetry operators for the linear Schr\"odinger equations with arbitrary number of spatial variables. We deduce determining equations for coefficient functions of such operators and consider in detail some cases when these equations can be explicitly solved. In addition, the complete group classification of the nonlinear Schr\"odinger equation is presented.