Poisson方程的一维最优系统和不变解
ONE-DIMENSIONAL OPTIMAL SYSTEM AND THE INVARIANT SOLUTIONS OF POISSON EQUATION

本文研究了Poisson方程的一维最优系统及其不变解问题.利用吴-微分特征列集算法，借助于Mathematica软件，计算了Poisson方程的古典对称，并构建了Lie代数的一维最优系统.同时，利用不变量法，获得了一维最优系统中一个元素对应的Poisson方程的不变解.得到的结果推广了Poisson方程的精确解.
In this paper, we discuss one-dimensional optimal system and the invariant solutions of Poisson equation. By using Wu-differential characteristic set algorithm with the aid of Mathematica software, the classical symmetries of the Poisson equation are calculated, and the one-dimensional optimal system of Lie algebra is constructed. And we obtain the invariant solution of the Poisson equation corresponding to one element in one dimensional optimal system by using the invariant method, which generalizes the exact solutions of the Poisson equation