Symmetric Classification Of A Class Of (2+1)-dimensional Differential Difference Equations

In recent years,the study of Lie symmetry algorithm is of great significance.Lie symmetry algorithm is also widely used in mathematics,computer,chemistry,physics,geology and other disciplines.In this letter,we have performed a symmetric classification study on a class of?2+1?dimensional differential-differential equations.First of all,the mathematical mechanization and related content of lie group are introduced.Next the steps of Lie symmetry algorithm involved in differential equation,difference equation and differential difference equation,and discusses the vector field,prolongation and group invariant solution of Lie pair method under its equation.After that,a class of generalized?2+1?dimensional differential difference equation is classified and studied by Lie pair weighting method.By solving the vector field of this kind of equation,then classifying the vector field,the reduced equations corresponding to the vector field are found respectively,and then the solutions are carried out.In addition,simple classifications are carried out in the case of high dimension by this method.Finally,the equation of form?u_n?_xt=F_n(u_n-1,u_n,u_n+1)is classified by this method,the symmetric algebra and reduced equation of equation?u_n?_xt=F_n(u_n-1,u_n,u_n+1)in low dimensional space are obtained.Taking equation Toda as an example,the symmetric algebra and reduced equation of equation Toda are obtained by classifying equation Toda.