Study On Some Exact Solutions Of Nonlinear Evolution Equations Based On Bilinear Transformation

Since the 1960 s,with the rapid development of science and technology,nonlinear science has been deeply studied and widely used in various natural sciences,including machinery,chemical industry,motor,energy,civil engineering,optical science,communication,biology,automatic control,materials,at the same time,emerged a large number of nonlinear evolution equation(abbreviated as NLEE).At present,nonlinear science has developed into an important modern discipline,which can better reflect the evolution of the objective world and explain the interrelation between individuals.It is becoming more and more important to model these nonlinear phenomena and find the exact solution of these NLEE.In order to obtain analytical solutions,many researchers have gradually established and developed many effective methods for solving NLEE in recent decades.Based on bilinear method,this thesis studies several kinds of exact solutions of high-dimensional nonlinear evolution equations(NLEE),namely,by solving the corresponding bilinear equations of NLEE,the breather wave solutions,periodic lump solitons,rational solutions,lump-type solutions and their interaction solutions are constructed to several types of high-dimensional nonlinear evolution equations by symbolic calculation.Using figures,we analyze their geometrical,physical and dynamic characteristics.The details are as follows:In the first chapter,the Hirota bilinear method and generalized bilinear method used in this thesis are introduced emphatically.In addition,the research status and development direction of the breather wave solutions,periodic lump solitons,rational solutions,high-order lump-type solutions and its interaction solutions are described.In the second chapter,the generalized bilinear equation of(2+1)dimensional generalized Calgero-Bogoyavlenski-Schiff equation is given based on the generalized bilinear method,and the breather wave solutions,periodic lump solitons,rational solutions,high-order lump-type solutions and its interaction solution of the equation are obtained by using Maple,and these solutions are further discussed.In chapter 3,the bilinear form of the(2+1)dimensional Hietarinta-type equation is firstly given based on the Hirota bilinear method,and the breather wave solutions of the equation are solved by using the symbolic computing software Maple,and the higher-order solution of the equation is further discussed.In chapter 4,with Maple,a symbolic computing software,based on generalized bilinear method,we calculated the breather wave solutions,higher-order lump-type solutions and its interaction solutions of(2+1)-dimensional p-g BKP equation.The physical properties of these solutions are discussed according to three-dimensional,contour and density maps.The fifth chapter summarizes the research content of this thesis,and also gives some prospects for the further research work.