Lump Solution,resonance Y-Type Solution And Hybrid Solutions For Several Partial Differential Equations

In this paper,the lump solution of(2+1)-dimensional combined pKP-BKP equation and the resonant Y type solution of(2+1)-dimensional generalized Caudrey-DoddGibbon-Kotera-Sawada(CDGKS)equation and their mixed solutions are mainly studied.Firstly,the bilinear forms of these two equations are obtained by Hirota bilinear method,and the N-soliton solution of the(2+1)-dimensional generalized CDGKS equation is further derived.Next,by directly constructing the function f,defining new restrictions,combining the long-wave limit method,mode resonance method and velocity resonance method,the lump solution,breather soliton and resonance Y type solution are obtained,and then the hybrid solutions composed of these local waves are obtained.The first chapter is mainly about the research background,research methods,present situation and the main work of this paper.In chapter 2,the function f is directly constructed in the form of quadratic function,trigonometric function and exponential function.And lump solution,breather soliton and the interaction between lump wave and soliton of the(2+1)-dimensional combined pKP-BKP equation are obtained.In chapter 3,based on the N-soliton solution,the resonant Y type soliton and hybrid solution of the(2+1)-dimensional generalized CDGKS equation are studied.In chapter 4,we introduce a new nonlinear superposition of the(2+1)-dimensional generalized CDGKS equation between lump wave and other types of local waves,in which the lump wave never interacts with other types of local waves or collides all the time.The fifth chapter is the summary and prospect.