一类Burgers-KdV方程的李群分析、李代数、对称约化及精确解  

Lie Group Analysis,Lie Algebra,Symmetric Reduction and Exact Solutions of a Class of Nonlinear Evolution Equations

作　　者：胡彦鑫 郭增鑫 辛祥鹏[1] HU Yanxin;GUO Zengxin;XIN Xiangpeng(School of Mathematical Sciences,Liaocheng University,Liaocheng 252059,China)

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《聊城大学学报（自然科学版）》2021年第2期8-13,共6页Journal of Liaocheng University:Natural Science Edition

基　　金：国家自然科学基金项目(11505090,11171041)资助。

摘　　要：应用李群分析的方法对一类Burgers-KdV方程进行研究,首先求出了该方程的李点对称,构建了一维李代数的最优系统,并利用对称将原方程约化成为了常微分方程,最后利用构造辅助函数展开法以及齐次平衡等方法得到了该方程的一些新的精确解。The Lie group method is used to analyze a class of nonlinear evolution equations.By using Lie symmetry analysis,the symmetries of the equations are obtained,and the partial differential equations are reduced to ordinary differential equations.Then the optimal system of one-dimensional Lie algebra is constructed.Finally we have obtained some new exact solutions by using the auxiliary equations expansion method.

关 键 词：BURGERS-KDV方程 李群分析 李代数 精确解 

分 类 号：O175.2[理学—基础数学]