Research On Lump Solution And Interaction Solutions Based On Hirota Bilinear Method

The precise solution of nonlinear partial differential equation and its solutions are always popular.At present,many methods for Solving Exact Solutions of nonlinear partial differential equations have been proposed and developed.In recent years,the study of Lump solutions,interaction solutions and kinky breather solutions has attracted wide attention,especially the construction and solution of higher-order solutions has become the focus and difficulty of the study of non-linear partial differential equations.In this paper,Lump solutions,interaction solutions and kinky breather solutions of some nonlinear equations are studied.After solving the Lump solutions of the equations by Hirota bilinear method,the interaction solutions and kinky breather solutions of the equations are obtained according to the Lump solution hypothesis.The main works of this paper are as follows: solving Lump solutions,interaction solutions and kinky breather solutions of(3+1)-dimensional KP equation and(2+1)-dimensional Ito equation;solving Lump solutions,interaction solutions and kinky breather solutions of(2+1)-dimensional and(3+1)-dimensional shallow water wave equation on the basis of generalized bilinear operators;and solving the interaction solutions and kinky breather solutions of a(3+1)-dimensional bilinear equation under Hirota bilinear and generalized bilinear conditions.In the first chapter,we introduce the study of exact solutions of nonlinear partial differential equations,the brief introduction of Hirota bilinear and generalized bilinear,and the simple explanation of Lump solution,interaction solution and kinky breather solution.In the second chapter,the bilinear equation of(3+1)-dimensional KP equation is given,and the Lump solution of the equation is solved by constructing the positive quadratic function method and Mathematica calculation software.At the same time,the interaction solutions and kinky breather solutions of the equation are further discussed.Similarly,the bilinear form of(2+1)-dimensional Ito equation is given first,and then several kinds of interaction solutions of the equation are given and solved.In Chapter 3,firstly,the bilinear forms of(2+1)and(3+1)-dimensional shallow water wave equations under generalized bilinear conditions are given.Secondly,the Lump solutions of the equation are solved by constructing the positive quadratic function method by Maple calculation software,and the interaction solutions and kinky breather solutions of the equation are further discussed.Chapter 4 introduces the interaction solutions and kinky breather solutions of a(3+1)-dimensional bilinear equation,and Lump solutions,interaction solutions and kinky breather solutions of the equation under generalized bilinear conditions.The last chapter briefly summarizes the main contents of this paper,and prospects the future research directions.