求微分差分方程李对称的非交换微分法

The Noncommutative Differential Methodology to Obtain the Lie Symmetry of Differential-difference Equations

利用微分形式和李导数,Harrison B K,Estabrook F B曾给出了求微分方程对称的一种几何方法.最近,该方法被推广到分析半离散微分方程的李对称中去.在本文中,我们利用一个完全不同的离散微分理想求得了微分差分方程的李对称.

By means of differential forms and Lie derivatives, Harrison B K, Estabrook F B have presented a methodology to find symmetries of differential equations. Recently, the method has been extended to analysis semi-discrete differential equations. In this paper, we use a different discrete differential ideal to obtain the Lie symmetry of the differential- difference equations.