Research On The Exact Solutions Of Several Mathematical And Physical Equations Based On Hirota's Bilinear Equation

Due to the wide application of mathematical physical equations in oceanography,nonlinear optics,electromagnetics and many other natural science fields,and the role of their exact solutions in describing natural phenomena,the study of exact solutions of mathematical physical equations has always been one of the important research topics of soliton theory.In this paper,we mainly study the bump solutions,strange wave solutions and interaction solutions of several mathematical physical equations.The structure is as followsIn the first chapter,the generation and development of soliton theory are introduced,and then the integrable system and related theories and methods are introduced.In Chapter 2,based on the Hirota bilinear equation and the simplified Hirota bilinear equation,we study the Rogue wave solutions and breathers of the equation.Then obtain the Complexiton solution and lump solutions of the CDGKS equation.In Chapter 3,we study the lump,lump-type solutions of a class of mathematical physical equations by positive quadratic function method.In Chapter4,we obtain periodic soliton,double soliton and Y-soliton solutions of the equation under the interaction of exponential function,trigonometric function and hyperbolic function.In this paper,the dynamic analysis of these sp ecial solutions with physical significance is also carried out.Finally,it summarizes and prospects the key research contents.