Abstract
For a variable coefficient Kadomtsev–Petviashvili (KP) equation the Lax pair as well as conjugate Lax pair are derived from the Painlevé analysis. The N-fold binary Darboux transformation is presented in a compact form. As an application, the multi-lump, higher-order lump and general lump-soliton interaction solutions for the variable coefficient KP equation are obtained. Typical lump structures with amplitudes exponentially decaying to zero as the time tends to infinity and interactions between one lump and one soliton are shown.
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