Dynamical analysis of rational and semi‐rational solution for a new extended (3 + 1)‐dimensional Kadomtsev‐Petviashvili equation

This paper proposes a new extended (3 + 1)‐dimensional Kadomtsev‐Petviashvili equation that portrays a unique dispersion effect about . Its integrability is confirmed via the WTC‐Kruskal algorithm in Painlevé sense. ‐soliton, breather, and ‐type solitary wave are derived systematically at first. Then, the mixed solution composed of soliton and breather is obtained. In addition, the “long wave” limit is employed to construct rational and semi‐rational solution. The rational solution can be classified as rogue wave, ‐type solitary wave, and lump wave. The semi‐rational solution has the form a hybrid of two solitons, a hybrid of rogue wave and soliton, a hybrid of lump and soliton(s), and a hybrid of lump and breather. The results may help simulate complex waves and their interactions in fluid.