CRE?CTE?Hirota Method And Interaction Solutions Of Some Nonlinear Evolution Equations

A large number of non-linear phenomena in the real world are modeled by using the non-linear evolution equations,so the study of non-linear evolution equations plays an important role in understanding and explaining non-linear phenomena.In particular,the studies on solving non-linear evolution equations can provide new methods and new solutions of the considered non-linear problems.The solutions of non-linear evolution equations obtained by the visualization,the analytical and the numerical methods can help people to describe and explain the essential properties of the non-linear phenomena which appear in different scientific fields.In this thesis,we shall mainly study the problem of solving non-linear evolution equations.Three popular methods,such as the CRE method,CTE method and Hirota method are used to construct the interaction solutions of some non-linear evolution equations.The contents of this thesis are composed of five chapters.The first chapter is the introduction,which mainly introduces the significance of the research works of the nonlinear evolution equations and the studies on the CRE method,the CTE method and the Hirota method at home and abroad.Finally,we shall introduce the main work of this thesis.In Chapter 2,the consistent Riccati expansion method(CRE)is applied to study the Boussinesq-Burgers equations and the consistent Riccati integrability of the Boussinesq-Burgers equations is proved.By solving the consistent equations,some exact interaction solutions of the Boussinesq-Burgers equations are given,which include the interaction solution between solitary waves and periodic elliptic waves and the solitoff-type solution.In Chapter 3,the consistent hyperbolic tangent function expansion method(CTE)is applied to the extended shallow water wave equation and(1+1)-dimensional KdV6 equation,and some exact interaction solutions of these two equations are given.These solutions include the interaction ofsoliton and periodic wave?the interaction solution of variable amplitude periodic wave,elliptic periodic wave and so on.In Chapter 4,the lump solutions of(3+1)-dimensional BKPBoussinesq equation are constructed by Hirota bilinear method.The necessary conditions for the parameters contained in the lump solutions to guarantee the analyticity,positivity and locality of the lump solitons are given.The interaction solutions of the lump solitons and kink solitons are obtained by adding an exponential function to the quadratic function solution.In addition,graphics are drawn to illustrate the dynamic characteristics of these solutions.The fifth chapter is the conclusion and the works which need to be studied in the future are briefly introduced.