Explicit Exact Traveling Wave Solutions For Two Classes Of Nonlinear Evolution Equations

The dynamic model described by nonlinear differential equations processing in a great variety of natural phenomena usually leads to nonlinear evolution equations, and solving the nonlinear evolution equations has become a hot research direction in the field of nonlinear science, in particular, the found of soliton solution, making the exact explicit solutions become a core problem. This paper mainly uses the bifurcation theory of dynamical systems to analysis the exact explicit traveling wave solutions of two kinds of nonlinear evolution equations. We acquire the dynamical behavior of generalized Schr?dinger-Boussinesq equations for the first time, and the equations are shown to have new parametric representations of solitary wave solutions and periodic cusp wave solutions.The structure of this paper is organized as follows.In Chapter 1, the introduction mainly expounds the research background, the current research status of traveling wave solutions of nonlinear evolution equations,and the main research contents of this paper.In Chapter 2, we introduce the main method of traveling wave solutions of nonlinear evolution equations: the bifurcation theory of dynamical systems, and some concept and nature about the elliptic functions.In Chapter 3, we investigate the dynamical behavior of K(2,-2,4) equation in specific parameter domain, and the exact explicit parametric representations of peakon are obtained.In Chapter 4, we study the dynamical behavior of the generalized Schr?dingerBoussinesq equations by using the method of the bifurcation theory of dynamical systems for the first time, and then obtain the new solitary wave solutions and periodic cusp wave solutions.Finally, we give a summary to the main contents of this paper, and put forward to the research work in the future.