Anomalous scattering of lumps for the extended Kadomtsev–Petviashvili equation arising in water wave

Abstract

The propagation path among lumps typically consists of straight lines after usual normal scattering. In this paper, we focus on the anomalous scattering of lumps for the extend Kadomtsev–Petviashvili equation by utilizing two distinct techniques. Based on these two methods, the lumps which possess equal amplitudes can experience the anomalous scattering, i.e., weak interaction. The binary Darboux transformation method is employed to obtain one type of anomalous scattering between lumps through choosing various parameters for lump solution. To explore more kinds of interactive behaviors of multiple lumps, we derive the anomalous scattering of multiple lumps as well as interactions between anomalously scattered lumps and other lumps or a line soliton by using the asymptotic approach. Two, three and five types of anomalous scattering appear respectively while two, three and four equal-amplitude lumps are involved in the weak interaction. The asymptotic approach can give the interaction between anomalously scattered lumps and a soliton apart from the interaction between lumps. The numerical results suggest that the weakly interacting lumps move along the curves and other waves keep their original trajectories just as the normal scattering.