Bifurcation Of Traveling Wave Solutions For The Generalized BKP Equations

In recent years, the study of nonlinear wave equation which reflect the problems ofphysics and chemistry has become a focus of scholars in various fields With the boom ofnonlinear science. How to solve the nonlinear wave equation has become an importantresearch topic in the field of nonlinear science for a lot of research scientists, which hasvery important theoretical value and practical significance.In this thesis，from the viewpoint of bifurcation theory of dynamical systems，weinvestigate the bifurcations of nonlinear wave equation. By making full use of the firstintegrals and phase portraits of integrable wave systems，we study the explicit and exacttraveling wave solutions of the nonlinear wave equations. Meanwhile，by using thequalitative theory of differential equation，we make an analysis of the existence ofsmooth and non-smooth traveling wave solutions which are difficult to obtain. This thesisconsists of five chapters.In chapter1，we summarize the historical background，researchdevelopments and significance of nonlinear wave equations.In chapter2，the basic theory and method of nonlinear wave equation arepresented.In chapter3，we investigate the generalized (2+1)-dimensional BKP equation byusing the bifurcation theory of planar dynamical systems. For different m、n，and a fixeda，When the parameters of c, g changes，we discuss and analyze their phase portrait andbranches，then，work out the solitary wave solutions, compactons, periodic cusp wavesolutions and periodic wave solutions of the equations.In chapter4，application of phase diagram study generalized (2+1)-dimensionalBKP equation of dynamics，the existence of the solitary wave solutions，compactons，periodic cusp wave solutions and periodic wave solutions，smooth and non-smoothperiodic wave solutions are given a sufficient condition for the existence in the parameterspace within different regions，and calculate the exact parameter expression.The last is the summary and the forecast， this paper summarize the work， putforward to solve the problem.