Anomalous Scattering and Weak Interactions of Lumps for the (2 + 1)-Dimensional Generalized Kadomtsev-Petviashvili Equation

In this paper, we study anomalous scattering and weak interactions of lumps for the (2+1)-dimensional generalized Kadomtsev-Petviashvili equation. Together with the long-wave-limit method, the normal scattering lump solutions are obtained. By adding perturbation terms to the normal scattering lump solutions, the anomalous scattering of two-lump and three-lump solutions is derived. The weak interactions among one soliton with two lumps, two solitons and two lumps as well as the interactions between one normal lump and two anomalous lumps are constructed. The dynamic properties of these anomalous scatterings and weak interactions are analyzed in detail. In these hybrid anomalous scattering solutions, from the long-time asymptotic behavior of the solutions, we find that the peak trajectories separate as t when |t|→∞. In particular, a head-on collision of two lumps leads to 135° scattering. Moreover, the anomalous lumps exhibit the same dynamical properties when they collide with solitons. The results described in this paper could also be generalized to the other (2 + 1)-dimensional integrable systems.