中文摘要：

借助符号计算软件Maple,根据微分方程单参数不变群和群不变解的概念,利用李群对称的待定系数法,得到Hunter-Saxton方程的包含5个任意常数和一个任意函数的一般形式的对称.通过该对称中任意的函数和常数的不同选取,将Hunter-Saxton方程约化为不同形式的常微分方程.最后对约化后的常微分方程进行变换求解,进一步得出Hunter-Saxton方程的一些群不变解和精确解.

英文摘要：

By using the symbolic computation software Maple,according to the concepts of single parameter invariant groups and group invariant solutions of differential equations, the general symmetry of the Hunter-Saxton equation was obtained with the help of its symmetry equation, which included five arbitrary constants and one arbitrary function. The Hunter-Saxton equation was reduced to some types of different ordinary differential equations by selecting different constants and function. Finally,with the transformational solving of the ordinary differential equations,group invariant solutions and exact solutions of the Hunter-Saxton equation were obtained directly.