一类二阶立方变系数微分算子的不变子空间

Invariant subspaces of a class of second-order cubic differential operators with variable coefficients

为了研究一类二阶三次变系数微分算子的不变子空间,本文借助符号计算系统Maple确定出这类二阶立方算子的不同维数的子空间,同时得到了一些二阶立方变系数偏微分方程的精确解.

In this paper,invariant subspace method is used to study a class of second‐order cubic differential operators with variable coefficients.Based on the symbolic computation system Maple,these differential operators admit invariant subspaces are described,as a consequence,the exact solutions to some nonlinear evolution equations with variable coefficients are obtained.