Residual symmetries, nth Bäcklund transformation and interaction solutions for (2+1)-dimensional generalized Broer-Kaup equations

Based on the residual symmetry theorem, the residual symmetry is obtained for the (2+1)-dimensional generalized Broer-Kaup (GBK) equations. The multiple residual symmetries are presented and localized by introducing prolonged systems, and then nth Bäcklund transformation for the GBK system in terms of determinant is derived. By means of the consistent tanh expansion (CTE) method, we get various interaction solutions which describe soliton interacting with other nonlinear waves including multiple resonant soliton wave, error function wave, periodic wave and rational function wave.