Painlevé analysis and special solutions of generalized Broer–Kaup equations

The (1+1)-dimensional Broer–Kaup system which describes the propagation of shallow water waves is extended to a generalized (2+1)-dimensional model with Painleve property. Some special exact solutions are obtained by using the truncated Painleve expansion. The generalized (2+1)-dimensional Broer–Kaup system also possesses quite rich localized excitations as other well-known (2+1)-dimensional integrable models. Especially, the elastic (pass through) interaction property without phase shift for two ring type solitons is graphically exhibited.