Residual Symmetry Reduction and Consistent Riccati Expansion of the Generalized Kaup-Kupershmidt Equation

The residual symmetry of the generalized Kaup-Kupershmidt (gKK) equation is obtained from the truncated Painlevé expansion and localized to a Lie point symmetry in a prolonged system. New symmetry reduction solutions of the prolonged system are given by using the standard Lie symmetry method.Furthermore,the gKK equation is proved to integrable in the sense of owning consistent Riccati expansion and some new Bäcklund transformations are given based on this property, from which interaction solutions between soliton and periodic waves are given.