轴对称波方程的Lie点变换群及其群不变解

Axisymmetric wave equation's one-parameter Lie group of transformations and group invariant solutions

首先用古典无穷小算法导出了由轴对称波方程的任意元和无穷小生成子的系数构成的超定线性偏微分方程组,即确定方程DE。其次借助符号计算机软件maple解方程组,求出了轴对称波方程的一些无穷小生成元,然后根据Lie第一基本定理求出了相对应的单参数Lie变换群;最后将所求得的无穷小生成元代入不变曲面条件,分别利用不变形式法和直接代入法求出轴对称波方程的群不变解。

First,an overdermined system of PDEs which is composed of the arbitrary element of axisymmetric wave equations and the coefficient of infinitesimal generators is derived by classical infinitesimal Lie method.Second,some infinitesimal generators of axisymmetric wave equation is given with the help of the symbols computer software Maple,and further the corresponding one-parameter Lie group of transformations is found out by the first fundamental theorem of Lie.Last,take the obtained infinitesimal generators into invariant surface condition,and then group invariant solutions of axisymmetric wave equation can be derived by use invariant form method and direct substitution method.