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

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.