Solutions of the (2+1)-dimensional high-order Broer-Kaup equation

In this paper we first revisit the Painleve integrability of the (2+1)-dimensional high-order Broer-Kaup equation. Then we get soliton and multi-soliton solutions by both the standard truncation of Painleve analysis and Conte´s truncation of Painleve analysis. Two Backlund transformations are obtained. A much more general kind of multi-soliton solutions are gotten by a special ansatz, which we will describe in detail in the paper.