广义KdV方程的对称约化和级数解

摘要

In nonlinear science,many problems described by the nonlinear evolution equations. It is particu-larly important to find out the exact solutions. In this paper,the Lie symmetry analysis is performed for the ex-tended KdV equation. By taking the Lie group method,the optimal system and the exact solutions from the symmetry transformations are provided. Such exact explicit solutions are important in both applications and the theory of nonlinear science.%在非线性科学中，很多问题通过非线性发展方程来描述，那么求出其精确解显得尤为重要。文中基于李对称理论分析了广义KdV方程，研究精确解的求解。首先获得有限维李对称，结合向量场的伴随表示构造了优化系统，其次基于对称约化，得到了包含行波解和级数解在内的精确解。