Solving The Differential Difference Equations, Lie Symmetries Of The Geometric Method

Lie group theory is an effective and useful tool for obtaining exact analytic solutions of differential equations.Harrison and Estabrook present a geometric approach to obtain the symmetries of differential equations,The main idea of their approach is based on exterior differential forms and Lie derivatives.For the study of symmetries of differential-difference equations,it has been paid more attention in recent years.In this paper,we present a new approach for finding the Lie symmetries of differential-difference equations,such as(2+1)-dimensional and inhomogeneous Toda equations,in the language of discrete exterior differential forms.It can be regarded as the extension of Harrison and Estabrook' approach.