Lie Symmetry Analysis,Exact Solutions And Dynamical Behaviors Of Two Classes Nonlinear Partial Differential Equations

In the field of nonlinear science, the study of exact solution is one of the most important research directions. It has attracted attentions of the mathematician-s、dynamicists and physicists. Studies on the bounded traveling wave solutions and dynamical behaviors play an important role in the field of nonlinear partial differential equations whose results are helpful to explain the physical phenomena of the nonlinear science. The Lie symmetry analysis method is a powerful tool for the study of non-linear partial differential equations(system). By combining with the dynamical system methods, not only many exact representation which are physical meaning can be ob-tained, but also some solutions with the dynamical behavior can be got. Based on the Lie symmetry analysis method and the planar dynamical system method, in this the-sis, the exact solutions of two kinds of basic equations(system) are studied:the exact solution and the dynamical behaviors of partial bounded traveling wave solutions of Boussinesq equations and Burgers equations.The main contents of this thesis are as follows:In the first part of this thesis, we mainly study the Lie symmetry analysis, exact solutions and the dynamical behavior of solitary wave solution for the nonlinear variant Boussinesq equations. Firstly, fifteen similarity reductions are obtained by using the classical Lie symmetry analysis method. Secondly, solitary wave solution, kink wave solution, periodic wave solutions and convergence of the power series form solutions are got by using planar dynamical system method and power series method. At the same time, we also present the relationship of solitary, wave solution and parameters.In the second part of this thesis, we mainly study the Lie symmetry analysis, exact solutions and the spectral stability of kink wave solution for the nonlinear Burgers equations. Firstly, four similarity reductions are obtained by using the classical Lie symmetry analysis method. Secondly, kink wave solution and convergence of the power series form solutions are got by using tanh function method and power series method. At the same time, we also proved that the kink wave solution is spectral stability using the energy estimation method.