中文摘要：

利用李对称方法求得高阶Extended Kd V（EKd V）方程的无穷小生成元,然后利用无穷小生成元求得2组不同的相似变换与相似解,再由相似变换和相似解将高阶EKd V方程约化为2个不同的常微分方程,并运用函数展开法对其中一个常微分方程求解,得到2个新的行波解,最后借助计算机绘出其图形,并讨论了最高阶色散项对解图像的影响。

英文摘要：

Lie symmetry method is used to obtain the infinitesimal generator of the higher-order extended Kd V equation,then two groups of different similarity transformations and similarity solutions are obtained by using the infinitesimal generator. The higher-order EKd V equation is reduced to two different ordinary differential equations by similarity transformation and similarity solution. Using the function expansion method to solve the ordinary differential equation,two new traveling wave solutions are obtained. Finally,graphics are drawn with computers and the influence of the highest order dispersion term on the image is discussed.