Abstract
Abstract 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 (2 N − 1)-soliton solutions of the (1 + 1)-dimensional HBK system are obtained. Both the N -fold Darboux transformation and (2 N − 1)-soliton solutions can be written explicitly in terms of Vandermonde-like determinants which are remarkable compactness and transparency.
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