Study On Soliton Solutions And Periodic Wave Solutions Of Some Nonlinear Evolution Equations

Nonlinear integrable systems are very important in physics and mathematics.More and more attention has been paid to them.Experts and scholars are more and more interested in the study of solutions of nonlinear partial differential equa-tions.The exact solutions of nonlinear partial differential equations are obtained by using different effective methods.The exact solutions extend the research field of non partial differential equations in many aspects.In many methods,Hirota bilinear method and generalized bilinear method play an important role in presenting soliton solutions.In this paper,based on bilinear method,several kinds of exact solutions of high-dimensional nonlinear evolution equations(NLEEs)are studied,The periodic wave solution,cross knot wave solution,bright and dark soliton solution,understood and bump solution and their reaction solution are constructed,and their geometric form,physical meaning and dynamic characteristics are analyzed by graphs:In the first chapter,the Hirota bilinear method and the generalized bilinear method used in this paper are introduced emphatically,and the research and develop-ment of periodic wave solution,cross knot wave solution,bright dark soliton solution,bump type solution and its reaction solution are expounded.In Chapter 2,based on the generalized bilinear method,the generalized bilinear form of(3+1)-dimensional Kadomtsev Petviashvili Boussinesq like equation is given,and the interaction solution,kink wave solution and bright dark soliton solution are obtained by using the symbolic computing software maple,and the geometry of the equation is analyzed by graph.In Chapter 3,based on the generalized bilinear method,the new three wave solu-tions and new periodic wave solutions of the(3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like equation are obtained by using the symbolic computation software maple.Meanwhile,the periodic wave solutions of the generalized(3+1)-dimensional shallow water wave equation are obtained.The trajectories and trends of the new three wave solutions and periodic wave solutions are analyzed graphically.In Chapter 4,based on the generalized bilinear method,the generalized bilinear form of the new(3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is given,and the higher-order lump type solution of the equation is obtained by using the sym-bolic computing software maple.At the same time,the higher-order lump type solution and its reaction solution of the new(3+1)-dimensional partial differential equation are calculated,The physical meaning and dynamic form of higher order bump type solution and reaction solution are analyzed by graph.In the fifth chapter,the content of this paper is summarized,and the future work is prospected.