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

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