Residual symmetry, CRE integrability and interaction solutions of the (3+1)-dimensional breaking soliton equation

Abstract

Residual symmetry of the (3+1)-dimensional breaking soliton equation is obtained and localized to a Lie point symmetry in a properly prolonged system. The general form of Lie point symmetry group and the corresponding symmetry reduction solutions of the prolonged system are obtained by using the standard Lie symmetry method, which include various interaction solutions between solitons and nonlinear background waves of the (3+1)-dimensional breaking soliton equation. Furthermore, the (3+1)-dimensional breaking soliton equation is proved to be integrable in the sense of having consistent Riccati expansion. Based on this property, some new Bäcklund transformations of the (3+1)-dimensional breaking soliton equation are obtained, from which interaction solutions between solitions and cnoidal waves are explicitly given.