变系数五阶非线性薛定谔方程的对称性分类
Symmetry classification of variable coefficient cubic-quintic nonlinear Schrödinger equations
摘要：
本文在等价变换的作用下，对含5个任意时空函数的变系数五次非线性薛定谔方程进行了李代数分类.结果表明，在真正的五阶非线性中，它们的对称群至多是四维的。当方程是三次型时，它只有五维（同构于伽利略相似代数gs（1）），当方程是五次型时，它只有六维（同构于薛定谔代数sch（1））。
英文摘要：
A Lie-algebraic classification of the variable coefficient cubic-quintic nonlinear Schrödinger equations involving 5 arbitrary functions of space and time is performed under the action of equivalence transformations. It is shown that their symmetry group can be at most four-dimensional in the genuine cubic-quintic nonlinearity. It is only five-dimensional (isomorphic to the Galilei similitude algebra gs(1)) when the equations are of cubic type, and six-dimensional (isomorphic to the Schrödinger algebra sch(1)) when they are of quintic type.
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