Symbolic Solution Of A Class Of Differential-difference Equations Based On Lie-B(?)cklund Transformation

In this paper,Lie and Lie-B(?)cklund transform are used to study the(2+1)-dimensional WGC equation and the Volterra lattice equation,and the infinite di-mensional Lie algebra and symmetry of these two equations are obtained.The thesis is divided into four parts:The first chapter introduces the research content,it mainly introduces the research background of the Lie symmetry and the Lie-B(?)cklund transform methods.The second chapter is preliminary knowledge,we described the basic concepts and principle algorithms of Lie groups,and discussed the Lie symmetry genera-tors?prolongation and invariant groups in differential,difference and differential-difference.In third chapter,we use Lie symmetry reduction procedure to study the(2+1)-dimensional WGC equation and the Volterra lattice equation.The infinite dimen-sional Lie algebra and symmetry of these two equations are obtained.The(2+1)-dimensional WGC equation is a rational differential-difference equation,so it is necessary to consider the denominator constraint in the process of reduction.We can not directly apply the discrete Lie symmetry reduction procedure to the non-linear discrete Volterra lattice equation,in order to solve this problem,we use a similar transformation method to convert it into an equation which can be used to performation symmetric reduction.As the main part of the thesis,some concepts and principle algorithms of the Lie-B(?)cklund transformation method of the differential-difference equation are described.At the same time,Lie-B(?)cklund transformation is used to study the(2+1)-dimensional WGC equation and the Volterra lattice equation,and the reduced equations of these two equations are obtained.