The Lump Solution Of The ANNV-like Equation And The Understanding Research

Exact solution of nonlinear partial differential equations of research has been an important part in the field of partial differential equations,an effective method is to transform the original nonlinear partial differential equation into Hirota bilinear for-m by using appropriate variable substitution based on Hirota bilinear method,and then the bilinear form is solved by constructing the basis function,Finally,the ex-act solution of the nonlinear partial differential equation is obtained by the inverse operation of variable substitution.The Hirota bilinear form is transformed from the-operator.On the basis of-operator,Professor Wenxiu Ma innovatively integrated the study of Bell polynomial theory into the bilinear equations and intro-duced the generalized bilinearD_pdifferential operator of odd order.In this paper,a new bilinear equation of(2+1)-dimensional ANNV equation and(2+1)-dimensional bSK equation is constructed by applyingD_poperator,and new nonlinear partial d-ifferential equations,namely(2+1)-dimensional ANNV-like equation and two types of(2+1)-dimensional(2+1)-dimensional bSK-like equation,are calculated based on the constructed bilinear form by Bell polynomial,and solved the lump solutions and rational solutions of three types equations using the symbolic computing software Maple.At the same time,by drawing and analyzing the image of the motion tra-jectory of the wave solution over time,the spatial,local and dynamic characteristics of the understanding can be more intuitively presented.This article consists of four chapters:The first chapter mainly describes the background of nonlinear differential e-quations and the development trend and application of exact solutions.The second chapter mainly introduces the Hirota bilinear method,Bell poly-nomial theory,and related concepts of logarithmic transformation.The third chapter mainly apply the odd-order differential operatorD_pand Bell polynomial theory to derive the(2+1)-dimensional ANNV-like equation,and cal-culate its lump solutions and rational solutions by constructing positive quadratic functions and higher order functions,and finally draw images to analyze the dy-namics of the solutions of the(2+1)-dimensional ANNV-like equation.The fourth chapter mainly applies the odd-orderD_poperator and Bell poly-nomial theory to derive two types of(2+1)-dimensional bSK-like equations,and calculate their lump solutions and rational solutions,and finally draw images to analyze the dynamics of the solutions of(2+1)-dimensional bSK-like equations...