中文摘要：

利用经典Lie群方法研究一类改进Boussinesq方程的Lie对称群的存在性及相应的群不变解,证明了改进Boussinesq方程存在3-参数的Lie对称群,并得到了该方程的一些行波解和非行波解.

英文摘要：

Applying the classical Lie symmetry method, we investigated the problem of determining the largest possible set of Lie point symmetries for an improved Boussinesq equation. The most general Lie point symmetry group of the improved Boussinesq equation was determined and the corresponding group-invariant solutions, such as travelling wave solutions were obtained.