Bilinear Equations Of The Constrained Discrete KP Hierarchy

The constrained discreteKP(cdKP)hierarchy is the discrete form of the constrainedKP(cKP)hierarchy.Its Lax operator,Lax equation,flow equations,dressing operator and wave function have been studied,but the bilinear identity has not been discussed.This thesis aims to give the bilinear identity of cdKP hierarchy.The first one is to present the history of integrable systems.Then the current research situation of cKP hierarchy is introduced,including its Lax operator,flow equation,wave function,bilinear identity.Next the difference operator is introduced into cKP hierarchy to the discuss additional symmetry,development equation and bilinear identity of cdkp hierarchy.Finally,the ralated properties of cqKP hierarchy are studied.It is the basis of the integrable natures,such as tau function,string equationand,Viraroso algebra.The results can not only provide some ties between integrable systems and quantum algebras,but also enrich the theory of the integrable system.Therefore,the research on bilinear identity is meaningful.