Apply Hirota Bilinear Method To Solve The Rational Solutions Of Two Kinds Of (2+1)-dimensional Soliton Equations

Solving soliton solutions is a hot spot for the study of the nonlinear partial differen-tial equations.With the development of soliton theory,a majority of soliton solutions are obtained.Such as lump solutions,semi-rational solutions,rational-like solutions,rogue wave solutions and so on.Rogue wave solutions have become a hot topic in the research of soliton theory in recent years due to its' unique characteristics and significant dam-age in the marine environment.Now,many researchers have obtained one-dimensional integrable equations' rogue wave solutions.Yet the solution of multi-dimensional soliton equations have more obvious characteristics and deeper physical significance,so solving the rational solutions and rogue wave solutions of these equations become increasingly important.Based on the different types of the Hirota bilinear method,we discussed the(2+1)-dimensional dispersive long wave system's hige-order rational solutions and the(2+1)-dimensional Hirota-Maccari system's rogue wave solutions.Chapter 1.Mainly introduced the background of soliton theory,major research methods,research status of the rational solutions and rogue wave solutiions.Firstly,on the background of soliton generation,development process,research and development status,we mainly introduced the method of Hirota bilinear.Then the present situation of development and research for rational solutions and rogue wave solutions are also deeply elaborated.Chapter 2.Studied the rational solutions of the(2+1)-dimensional dispersive long wave equation.Firstly,new function is applied according to homothetic transformation,and then the orginal equations are transformed into the equal bilinear equations.By using the(?)function,we can obtain the N-order rational solutions.Based on the generalized,two-order and high-order rational solutions' blame collisions,a detail analysis of the dynamics is given.Chapter 3.Studied the rogue wave solutions of the(2+1)-dimensional Hirota-Maccari equation.Firstly,expanding the equation to the(3+1)-dimensional equivalent equation by introducing a new variable degradation conditions.And then,basis bilinear equations are transformed into equivalent equations by variable substitution.Last,the rational solutions and rogue wave solutions are obtained by using the differential iterative operators that satisfied the degradation conditions.Finally,by adjusting the value of the free variable,the high order rogue wave solutions of the original equations are obtained Chapter 4.Made a summary,induction and outlook for the thesis.