中文摘要：

为了研究Rosenau-Hyman方程的Lie对称及精确解问题,首先利用Lie对称方法分析其偏微分形式,得到Rosenau-Hyman的Lie对称群以及此对称群所对应的行波解;其次利用Jacobi椭圆函数试探法得到该方程的精确解.这些解对进一步研究Rosenau-Hyman方程所描述的物理现象具有一定的应用价值.

英文摘要：

A systematic investigation to derive the Lie symmetries and exact solution of RosenauHyman equation is presented.First of all,the symmetry group of Rosenau-Hyman equation is given with the help of Lie symmetry method and its partial differential form,and further the corresponding traveling wave solution is found out.Second,the exact solutions are obtained with the heuristics of the Jacobi elliptic function.These solutions have extensive application values to further research about some physical phenomenon which are described by the Rosenau-Hyman equation.