Rogue lumps on a background of kink waves for the Bogoyavlenskii–Kadomtsev–Petviashvili equation

In this paper, rogue lumps on a background of kink waves for the Bogoyavlenskii–Kadomtsev–Petviashvili equation are investigated. The Kadomtsev–Petviashvili hierarchy reduction method connected with the Hirota bilinear method is applied to obtain a new family of determinant semi-rational solutions to the Bogoyavlenskii–Kadomtsev–Petviashvili equation. Semi-rational solutions consist of rogue lumps and kink waves. These solutions possess abundant and interesting dynamics. The rogue lumps arise from the kink waves background, then exist in the background of kink waves at an extremely short period of time, and finally entirely decay back to the background of kink waves in the form of lumps, which are really localized in the two-dimensional space as well as in time. The results are helpful to study rogue lumps arising from the kink waves background of the higher dimensional complicated integrable systems.