Nonlocal Lie Symmetry Analysis Of A Class Of Differential Difference Equations

In this paper,the differential-difference non-local symmetry method is pro-posed to solve the differential-difference equation.This method is applied to two kinds of Toda lattice equations.The determining equations of the two equations are obtained by using the non-local symmetry method.With the results of the determining equations we get the corresponding non-local symmetries and reduc-tion equations.Compared with the classical Lie symmetry method,this method does not need to find the invariant condition and the invariant solution of the e-quation,which makes the operation more convenient and the forms of symmetries more abundant.As a result,we can get more solutions of the differential difference equation.The thesis is divided into three parts:The first chapter is the introduction,which mainly deals with the research content,historical background,development history and the simple introduction of differential-difference equation of non-local symmetry and Lie symmetry.The second chapter,mainly about the non-local symmetry Lie group and some of the concepts and principles of algorithm.Two aspects including the differential and differential difference Lie theory are discussed for the formation of generator,symmetric extension and invariant group,and non-local symmetry from the differ-ential to differential-difference respectively.As the main part of the thesis,the last chapter gives the applications of the non-local symmetry.Finally,a series of non-local symmetries are obtained by the method.