The Application Of The Differential Feature Column Method In Differential Lie Symmetry

In recent years,the characteristic set methods are successfully used in me-chanical proving?mechanics?theoretical physics and many other high-tech fields,such as robotics?mechanisms?computer vision?CAD.Lie symmetry has impor-tant theoretical and practical significance.in maths,physics,mechanics and other numerous disciplines.Its applications are very broad,such as algebraic topolo-gy?differential geometry?theory of controls?classical mechanics?quantum me-chanics?theory of branch?special function?relativity theory?continuum mechan-ics of solids and many other applications fields.The thesis is divided into three parts:The first chapter introduces the research content,historical background,develop-ment process of mathematics mechanization and Lie symmetry method,and the characteristic set,method of differential-difference polynomial system.In chapter two the concepts and principle algorithms of the characteristic set method which is used in the differential-difference polynomial system are introduced at first.And then we described the basic concepts of Lie groups,discussed the Lie symmetry generators?prolongation and invariant groups in differential,difference and differential-difference.As the main part of the thesis,the last chapter discusses the combination of difference characteristic method and Lie symmetry method,By the characteristic set method of D-D systems the coupled Toda lattice equation can be divided into some more easy triangular column which can be calculated easily.First,we used the zero decomposition theorem to divide the coupled Toda lattice equation into three characteristic series.Then,the invariant,groups and group invariant solutions of the characteristic series were obtained Lie symmetry method,According to the zero decomposition theorem,the group invariant solutions of the characteristic series and the coupled Toda lattice equations are the same.By using the Lie symmetry method,More solutions will be obtained.