The Geometry Method For Finding The Lie Symmetries Of Differential-difference Equations

Lie group theory is an efective and useful tool for obtaining the analytical solutionsof diferential equations.In shortly,the symmetry group of diferential equations is a trans-formation group,which transformed one solution of diferential equations to another.Howto find the symmetries of diferential-diference equations has been become a focus forresearchers in recent years.In this paper,on the basis of the previous work we will give outa further research on this question.In this paper,we will list the geometric method given by Harrison and Estabrook.Themethod is mainly use the exterior diferential forms and the Lie derivative to find the Liesymmetry.we will use the discrete exterior diferential to promote and apply,introduce thesemi-discrete exterior diferential form of only a discrete variable and multiple continuousvariables. At last,the (2+1)-dimensional Toda equation is given to explain this methodof seeking semi-discrete Lie symmetries specifically.