The Symmetry Of The Nonlinear System Of Symbolic Computation Algorithm And Its Application

Based on the mathematics mechanization thought of the renowned mathematician Wenjun Wu, this thesis takes the symbolic computation software as the tool to present a constructive method revolved the nonlinear partial differential system's Lie point symmetry, the Lie transformation group and the partial differential system's symmetry reduction. According to this method, we propose the LiePS and LiePSS software packages to resolve the (1+1) dimensions nonlinear partial differential (PDE) and retain the PDEs'Lie point symmetry, Lie symmetry group, symmetry reduction and their similarity solutions.Chapter 1 is a brief review of the computer algebra and computer algebra system, mathematics mechanization and the symmetry theory of differential equation. Simultaneously I introduce the domestic and foreign scholars achievements obtained in this discipline domain. My main works are listed at last.Chapter 2 mainly describes three traditional methods in the symmetry reductions of nonlinear differential equations:the classical Lie group method, non-classical Lie group method and CK direct method.Chapter 3 introduces the Lie transformation group, the first fundamental theorem of Lie, some of the basic concepts of differential equations and the invariant theorem, then based on the traditional Lie Group theory and methods, with the help of symbolic computation system Maple, I introduce a new method, so called direct computer algebra substitution method, which I applied to three nonlinear partial differential equations (group) for solving Lie point symmetry of non-linear partial differential equations, Lie symmetry group and its symmetry reduction.Chapter 4 takes advantages of the new method described in the chapter 3 and programs to implement the fully automated Lie Maple package for constructing the Lie point symmetry, Lie symmetry group and the symmetry reduction of (1+1) dimensional partial differential equations.The last chapter concerns the summary and discussions for the whole dissertation, as well as the prospect for those methods.