Multi-pole lump solutions and anomalous scattering in the BKP equation

This study investigates the dynamics of multi-pole lump solutions and their scattering phenomena in the Bogoyavlenskii–Kadomtsev–Petviashvili (BKP) equation. Utilizing the inverse scattering transform method, we generate standard M-lump solutions from eigenfunctions with simple poles and derive non-standard lump solutions associated with higher-order poles in their eigenfunctions. While standard M-lump waves exhibit normal scattering phenomena, multi-pole lump waves display time-dependent velocities and non-trivial scattering angles, referred to as anomalous scattering. Notably, this research introduces a novel triple-pole lump solution in the BKP equation. These anomalous scattering phenomena differ from those observed in the Kadomtsev–Petviashvili equation but exhibit similarities to those in the Davey–Stewartson system.