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Recently, a new decomposition of the (2+1)-dimensional Kadomtsev Petviashvili (KP) equation to a (1+1 )-dimensional Broer-Kaup (BK) equation and a (1+1)-dimensional high-order BK equation was presented by Lou andHu. In our paper, a unified Darboux transformation for both the BK equation and high-order BK equation is derivedwith the help of a gauge transformation of their spectral problems. As application, new explicit soliton-like solutionswith five arbitrary parameters for the BK equation, high-order BK equation and KP equation are obtained.