Research On Lump Solution, Blending Solution, Strange Wave Solution And Understanding Of (2+1) Dimensional Generalized BK-like Equation

Through some effective variable transformations,many partial differential e-quations of nonlinear system could be rewritten in Hirota bilinear form.The Hi-rota bilinear method is an efficient tool to obtain some of these solutions.At the same time,the Hirota D-operator plays a very important role in solving solutions to nonlinear partial differential equations.Professor Ma Wenxiu proposed a new kind of bilinear differential operator D_p and explored that the linear superposition principle and Bell polynomial could apply to the corresponding bilinear differential equations under some conditions.Therefore,by using the definitions and properties of generalized bilinear operations with a prime number p=3,we introduced the(2+1)-dimensional generalized Bogoyavlensky-Konopelchenko-like equation(g BK),(3+1)-dimensional Hirota-Bilinear-like equation(HB)and(2+1)-dimensional Ito-like equation,In addition,the lump solutions,interaction solutions,rogue solutions and rational solutions of the equations are solved in this paper.Simultaneously,in or-der to illustrate the dynamical feature of the solutions with specific values of the involved parameters,some images are plotted.This article consists of five chapters:The first chapter mainly describes the background of mathematics mechaniza-tion,the development of nonlinear partial differential equations and the research direction and application fields.The second chapter mainly introduces some concepts involved in this article,Such as Hirota bilinear method,linear D_p-operator and Bell polynomial.Chapters 3,4,and 5 used Hirota bilinear method to derive three new equation-s,they are the(2+1)-dimensional generalized BK-like equations,(3+1)-dimensional HB-like equations and(2+1)-dimensional Ito-like equations.Under D₃ operator,their corresponding bilinear equation are obtained.By the help of Maple,we get their lump solutions,interaction solutions,rogue wave solutions and rational solu-tions.