Traveling Wave Solutions And Dynamical Behavior Of Some Nonlinear Wave Equations

With the development of nonlinear scientific research,solving nonlinear equations becomes one of the core problems in nonlinear science.In this thesis,we first introduce the research background of nonlinear wave equation,bifurcation theory and preliminary knowledge.Then,by applying simple symbolic calculation method,we get rational solutions and rogue wave solutions for a class of(3+1)-dimensional KdV equation.Furthermore,by using bifurcation theory of dynamical system,we obtain exact solutions and its phase portraits of GKP equation,the nonlinear coupled of Klein-Gordon equations and the ac-driven Ginzburg Landau equation.This thesis is organized as follows:In the first chapter,we mainly introduce the background of nonlinear wave equation,traveling wave solutions,bifurcation theory of nonlinear wave equation and the prereliminaries.In the second chapter,by using a simple symbol calculation method,we obtain rational solutions and rogue wave solutions of this equation.In the third chapter,by using the theory of dynamic system,we get bifurcation and phase portraits of GKP equation and by discussing parameter range,we get all rational forms of exact solutions.Including solitary wave solutions,periodic wave solutions,kink wave solutions and breaking wave solutions.In the fourth chapter,the theory of dynamical system is applied to discuss the traveling wave solution of the nonlinear coupled of Klein-Gordon equations under different parameters.In the fifth chapter,we study the high order ac-driven Ginzburg-Landau equation and obtain the exact solutions with different parameters.