Differential Lie Symmetry Analysis And Symbol Calculation Based On Characteristic Sequence Method

The characteristic set method is the core algorithm of mathematical mecha-nization theory.It has been applied to many fields such as machine proof theorem,equation solving and digital control.Symmetry theory plays an important role in the study of nonlinear differential-difference equations.The Lie symmetry method is exactly a powerful tool for studying the symmetries of equations.The core idea of this paper is to combine the characteristic set method with the Lie symmetry method.Firstly,the Lie symmetry method is used to get the determining equation-s.Then,determining equations are solved by the characteristic set method.Thus,we can obtained the vector field and exchange relationship of nonlinear differential-difference equations.This article consists of three chapters:The first chapter is the introduction.It mainly discusses the research content,historical background,and development history of mathematics mechanization and Lie symmetry method.Besides simple introduction of differential-difference charac-teristic sets.The second chapter is preliminary knowledge.It mainly discusses some con-cepts and principles of differential-differential characteristic sets and Lie groups.It discusses generators,continuations and invariant groups of Lie symmetries,and introduces the theory of symmetry algorithm for differential-difference equations which based on the characteristic set method.The third chapter is the core of this paper.It combines the differential charac-teristic set method and the Lie symmetry method,and obtains determining equa-tions by using the commuting flow method in the Lie symmetry theory.Then,the vector field and exchange relation between the Langmiur chains and Klein-Gorden equations are obtained by using the differential characteristic set method.