Residual Symmetries And Interaction Solutions For Three Types Of Integrable Systems

As an important branch of nonlinear science,nonlinear partial differential equations have been widely concerned and studied by scholars.Among them,integrable systems generally have some good properties.Recently,the residual symmetries and consistent Riccati expansion method proposed by professor Lou have been used to obtain new exact solutions of nonlinear evolution equations.In this thesis,these two methods are mainly used to construct the symmetric reduction solutions and interaction solutions of the systems.This paper mainly includes the following four chapters:Firstly,the background of the soliton theory of nonlinear evolution equations is introduced,as well as the achievements made by domestic and foreign scholars,then briefly explains the methods used in this research,and clarifies the main work of this paper.In chapter 2,the residual symmetries and B(?)cklund transformation theorem of the modified Degasperis-Procesi equation are obtained by truncated Painlevé expansion method.Then,the soliton solutions of the system and the interaction solutions of solitary wave and elliptic periodic wave are established by using the consistent Riccati expansion method,and the obtained interaction solutions.In chapter 3,the residual symmetries and CRE solvability of the(2+1)dimensional Tu equation are studied,and we obtain the corresponding symmetries groups transformation theorem.Then,B(?)cklund transformation theorem and the new interaction solutions of the system are constructed.In chapter 4,we obtain the corresponding symmetries groups transformation theorem of the(1+1)dimensional Sharma-Tasso-Olver equation by analyzing its residual symmetries,and localize the residual symmetries to Lie point symmetries by prolonging the original system to a lager one.Then,using the CRE method to construct the new interaction solutions of the system.