Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

Abstract

Two (3+1)-dimensional shallow water wave equations are studied by using residual symmetry and consistent Riccati expansion (CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. CRE method is carried on the two equations to obtain new Bäcklund transformations from which a type of interesting interaction solutions between solitons and periodic waves is generated.