Abstract
In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a (1+1)-dimensional Broer–Kaup (BK) equation and a (1+1)-dimensional high-order Broer–Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new basic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev–Petviashvili (KP) equation are obtained.
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