Exact Solutions Of Some Nonlinear Evolution Equations:Bilinear Method

In this thesis,the Hirota method is used to solve the nonlinear evolution equations,which is the key and difficult point in the development of soliton theory,exact solutions such as soliton solution,Lump solution and interaction solution are constructed by using test function.In chapter 1,the research background of this thesis,especially the progress of Soliton and integrable system is introduced.Secondly,some research methods and some exact solutions of nonlinear evolution equations are introduced,including rogue wave solution,Lump solution and breather solution.At last,the thesis gives a brief introduction to the computer symbolic computation and the main work of this thesis.In chapter 2,we study the(2+1)-dimensional shallow water wave equation derived from the generalized Hirota-Satsuma-Ito equation introduced by Sakkaravarthi.By using bilinear methods and testing functions,a large number of exact solutions are constructed,such as soliton solutions,Lump Solutions and Lump-periodic solutions.In chapter 3,we aim at solving two kinds of nonlinear evolution equations,including a(3+1)-dimensional nonlinear evolution equations and a four-dimensional sixth-order bilinear equations.The effectiveness of the Hirota method combined with the test function is verified.The results show that the combination of Hirota bilinear method and test function is an effective and powerful mathematical tool for solving exact solutions of high dimensional nonlinear partial differential equation.In chapter 4,we give the conclusion and prospect of this thesis.