Kadomtsev–Petviashvili equation with self-consistent sources: breathers, lumps and their interactions

Under investigation in this paper is the Kadomtsev–Petviashvili (KP) equation with self-consistent sources. We adopt two different bilinear systems which require different KP hierarchy reductions to construct the corresponding breather solutions in Gramian determinant. Then, we construct two distinct categories of breather solutions, and show that both types are the same only under the condition \(a=\alpha =0\) $a=\alpha =0$ . Furthermore, employing the long-wave limits to breather solutions, we obtain some rational and exp-rational solutions, which reveal various nonlinear interactions, including between two lumps, between a lump and a breather and between a lump and a soliton. Space-localized “dark” and tetrapetalous-type breathers and lumps are also addressed. Interactions between the above hybrid waves is of fundamental importance in the understanding of high-dimensional nonlinear phenomena of extreme ocean waves and in other fields such as solid state physics and plasma physics.