Painlevé analysis for a new (3 +1 )-dimensional KP equation: Multiple-soliton and lump solutions

Abstract

Abstract The current work proposes a new (3 + 1)-dimensional Kadomtsev-Petviashvili (KP) equation ((3 + 1)-KPE). We verify the integrability of this equation using the Painlevé analysis (PA). The bilinear formula is applied to the extended KPE to explore multiple-soliton solutions. Also, we formally establish a class of lump solutions using distinct values of the parameters.