Explicit N-fold Darboux transformation and multi-soliton solutions for the (1 + 1)-dimensional higher-order Broer–Kaup system

In this paper, we present a new N-fold Darboux transformations of the (1 + 1)-dimensional higher-order Broer–Kaup (HBK) system with the help of a gauge transformation of the spectral problem. As an application, new explicit (2N − 1)-soliton solutions of the (1 + 1)-dimensional HBK system are obtained. Both the N-fold Darboux transformation and (2N − 1)-soliton solutions can be written explicitly in terms of Vandermonde-like determinants which are remarkable compactness and transparency.