Analytical Solutions Of Several Class Of Nonlinear Differential-difference Equations

The nonlinear differential difference equation is widely used in mathematics,physics,biology,economics and other research fields.Over the years,people have developed many methods for solving nonlinear differential difference equations,such as the inverse scattering method,Darboux transformation method,exponential function method,elliptic function method and so on,and many analytical solutions with special significance have also been obtained.In this paper,the exponential function method and Darboux transform method are used to study the analytical solutions of three types of nonlinear differential difference equations.Different types of solitary wave solutions of the equation are obtained,and their properties are analyzed by numerical experiments.The concrete content of this paper is divided into the following four parts.The first part introduces the relative background of the nonlinear differential difference equation and some methods for solving analytic solution,especially soliton solutions related content.The second part mainly introduces the research methods involved in this paper: exponential function method and Darboux transformation method.The third part is the main work of this paper.The generalized KvM equation and the modified Volterra lattice equation are studied by using the exponential function method,and two different types of solitons are obtained.By constructing the Darboux transformation,the analytical solutions of a class of Lax integrable differential difference equations are obtained.Combined with numerical experiments,the properties of the solutions are analyzed.