Rational Solution And Lump Solution Of A Class Of Nonlinear Evolution Equations And Interaction Between Them

Exact solutions of nonlinear evolution equations play an important role in scientific research.So far,the methods of solving nonlinear evolution equations are many,and the exact solution's type is diverse too.This paper mainly study the rational solutions,lump solution and interact-ion between different solutions of(2+1)dimension Boiti-Leon-Manna-Pempinelli equation(hereafter called the BLMP equation)by using the hi-rota bilinear method.The first chapter introduces the birth and development of soliton theory,integrable system,integrable coupling,the exact solution of nonli-near evolution equations,and the application background of soliton theory.The second chapter presents the general theory and method for related to this topic,mainly includes the hirota bilinear method,the important differential operator in bilinear method:D-operator,rational transformation,logarithmic transform and the method of obtaining the N-soliton solution of bilinear equation by using parameter perturbation.The third chapter.According to the generalized hirota bilinear meth-od proposed by professor Wenxiu Ma,the(2+1)dimension BLMP-like equation was derived.Later we apply the direct method,parameter pertur-bation method to obtain the rational solutions and the N-soliton solution of equations.The fourth chapter has been further got the evolution breather,lump solution and rogue wave of(2+1)dimensional BLMP equation by using two-function method.And we study the interaction between its different solutions.It showed that a series of interesting and complex dynamic behavior.Then,we visualize their dynamic behavior by the 3d image.