| With the development of science and technology,the core of modern sci-entific research has gradually turned to nonlinearity from linearity.Nonlinear evolution equation can not only describe a lot of natural phenomena,dynamic system and the changing law of things,but also provide important enlighten-ments for many application problems,which plays a very important role in the research of related science and technology.However,the nonlinear system has no unified solving method,which is different from linear system.It often needs to be solved case by case.Therefore,the solution of nonlinear equation has been an important subject of the research of physicists and mathematicians for a long time.So far,there have been a lot of methods for the solution of nonlinear equation,for example:Mixed Exponential Method,Modified Simple Equation Method,Inverse Scattering Method,Hirota’s Bilinear Method,Invariant Sub-space Method,etc.With the development of various kinds of method,not only the equation that is difficult to be solved has been solved,but also the new solution with important physical significance are unceasingly found through the new method.This paper mainly took the CTE Method as background,on the basis of CTE Method solving the travelling wave solutions,use CRE Method learning two types of nonlinear equations,and solved its new interaction solution.The paper could be divided into four chapters,with the detailed arrangement as follows:the first chapter is introduction.Simple described the development of solitary wave and described the importance of nonlinear equations in mathematical physics,as well as the importance of solving the exact solution;The second chapter introduced the CRE Method and its solving steps,and then proved that the(1+1)dimension Boussinesq-Burgers equations is solvable by the CRE Method and the CTE Method;the last,the paper analyzed the tanh solution of the Boussinesq-Burgers equations;the third chapter,proved the(2+1)dimension Bogoyavlenskii equations is solvable by CRE,and solved its interaction solution;and the fourth chapter stated the summary and outlook. |
