New Traveling Wave Solutions For Two Kinds Of Nonlinear Equations

In this thesis we study the traveling wave solutions of the generalized fifth-orderKdV equation and the Burgers-Poisson equation. By using auxiliary equation method,we get new and more exact traveling wave solutions of the generalized fifth-order KdVequation. These solutions include solitary wave solutions, blow-up solutions, periodicblow-up solutions. For the Burgers-Poisson equation, we get several traveling wavesolutions by using bifurcation method and qualitative theory of dynamical systems.The main research work is as follows:In Chapter 1, we summarize the historical background, research developments, mainmethods and achievements for seeking exact solitary wave solutions.In Chapter 2, we use the auxiliary equation method to study the generalizedfifth-order KdV equation. With the help of the software Mathematica, nineteen solutionsare obtained. These solutions include solitary wave solutions, blow-up solutions, periodicblow-up solutions. Further, the auxiliary equation method is extended. The results hadbeen published on Journal of Southwest University for Nationalities(Natural ScienceEdition).In Chapter 3, the Burgers-Poisson equation is studied. First of all, the introductionof the Burgers-Poisson equation and the prior knowledge needed are presented, theprior knowledge is mainly used to draw phase portraits of planar system. By using thequalitative theory of di?erential equations and bifurcation method of dynamical systems,we get several new solutions.At last, the summary of this thesis and the prospect of future study are given.