Rogue waves of a (3+1)-dimensional BKP equation

Abstract In this paper, we investigate certain rogue waves of a (3 + 1)-dimensional BKP equation via the Kadomtsev-Petviashili hierarchy reduction method. We obtain semirational solutions in the determinant form, which contain two special interactions:(1) one lump develops from a kink soliton and then fuses into the other kink one; (2) a line rogue wave arises from the segment between two kink solitons and then disappears quickly. We find that such a lump or line rogue wave only survives in a short time and localizes in both space and time, which performs like a rogue wave. Furthermore, the higher-order semi-rational solutions describing the interaction between two lumps (one line rogue wave) and three kink solitons are presented.