Lump Solutions And Integrability Analysis Of Two Types Of Nonlinear Equations In Generalized Bilinear Algebr

This article proposes an equation-like form based on the basic definition and properties of the generalized Hirota bilinear form under the₃operator.Then,by setting1)to be a fixed function form and performing symbolic calculations,the logarithmic variable substitution is used to obtain the exact solution of the nonlinear partial differential equation.Finally,we obtain lump solution and rational solution of the corresponding like equation.By using（2+1）-dimensional g CBS equation,The（2+1）-dimensional g KDKK e-quation and the（3+1）-dimensional g KDKK-like,new Bilinear forms are constructed for the（2+1）-dimensional constant coefficient g CBS equation,the（2+1）-dimensional constant coefficient g KDKK equation,the（3+1）-dimensional constant coefficien-t g KDKK equation and（2+l）-dimensional variable coefficient GKP equation.We mechanize symbolic computation by using Maple.At the same time,by describing the wave diagram,the images of various motion trajectories of the wave solution varying with timeare analyzed,showing clearer dynamic characteristics of the solution and specific location characteristics of special points on the wave diagram.This paper can be divided into four parts:In the first chapter,we describe the background and definition of mathematical mechanization and nonlinear partial differential equations,the current development of exact solutions.In the second chapter,the basic nonlinear theories in this paper are introduced,including generalized Hirota bilinear method,Bell polynomial theory and logarith-mic transform.In Chapter 3,we discuss the lump-like and rational solutions of the g CBS-like equation with constant coefficients,and derive the（2+1）-dimensional g CBS-like equation by using the theory of differential operators₃and Bell polynomials.The（2+1）and（3+1）dimensional g KDKK-like equations with constant coefficients are derived,and the lump solutions and rational polynomial solutions are calculated.Then various graphs corresponding to the waves are depicted and the dynamic properties of the solutions of the（2+1）dimensional g KDKK-like equations are analyzed.In Chapter 4,we mainly discuss the lump solutions of the variable coefficien-t like equation.By using the prime order₃operator and Bell polynomial theory,we derive the variable coefficient（2+1）dimensional GKP-like equation and calculate the lump-like solutions.Then we describe the various images corresponding to the waves and analyze the kinematic properties of the solutions of the（2+1）-dimensional variable coefficient GKP-like equation.