一个(2+1)-维推广KdV6方程的李对称分析  

Lie Symmetry Analysis of a (2+1)-Extensive KdV6 Equation

作　　者：苏丹 SU Dan(Department of Mathematics of Zhanjiang Preschool Education College,Zhanjiang 524084,China;Foundation Education Institute,Lingnan Normal University,Zhanjiang 524037,China)

机构地区：[1]湛江幼儿师范专科学校,广东湛江524084 [2]岭南师范学院基础教育学院,广东湛江524037

出　　处：《长春师范大学学报》2022年第6期15-18,共4页Journal of Changchun Normal University

基　　金：湛江市非资助科技攻关计划项目“关于拟线性中立型微分方程解的性质的研究及其应用性”(2021B01506)。

摘　　要：通过李对称方法研究了一个(2+1)-维的KdV6方程,给出了该方程所拥有的李对称无穷小生成元,计算确定了对应的有限维李代数的一维子代数最优系统.利用获得的最优系统对原(2+1)-维方程进行对称约化,将其约化为(1+1)-维方程,并再次对(1+1)-维方程进行对称约化得到常微分方程,利用截断展开法求解该常微分方程,得到了原(2+1)-维方程的精确解.In this paper,we study a (2+1)-extensive KdV6 equation by the Lie symmetry method.The infinite Lie symmetry generators are found and its one optimal Lie sub-algebra system is constructed.Then,the (2+1)-dimensional equation is reduced into (1+1)-dimension via the optimal system.And further reduction with its symmetry for the (1+1)-dimension reduced equation is presented and we obtain the an ordinary differential equation.The exact solutions are obtained by solving the ordinary (2+1)-equation using truncation method.

关 键 词：李对称 (2+1)-维KdV6 李代数 精确解 

分 类 号：O152[理学—数学]