Bifurcations Of Exact Solutions For Several Classes Of Nonlinear Evolution Equations

In this paper,the method of dynamical systems is used to study the bifurcations and exact solutions of several types of nonlinear evolution equations.Besides,we search the dynamical behaviors of these nonlinear mathematical and physical equations.In the first chapter,we introduce the development history of nonlinear water wave equation and the current situation at home and abroad on topics related to the equations we study.We also introduce the method of dynamical systems to solve nonlinear wave equations proposed by Professor Li Jibin.Based on the method of dynamical systems,in the second chapter we study the exact solutions of the generalized combined sinh-cosh-Gordon equation and triple sinh-Gordon equation.For generalized combined sinh-cosh-Gordon equation,we derive the explicit exact solutions under different parameter conditions by using traveling wave transformation.For triple sinh-Gordon equation,the implicit solution is derived by employing an intermediate transformation.In the last chapter,we conclude the work we do in this paper.We also propose the questions which need to be studied further in the future.