Anomalous Scattering of Lumps and Interaction of Lump Chains in the Modified Kadomtsev–Petviashvili‐I Equation

ABSTRACT This paper presents a systematic study of lump solutions and lump chain solutions in the modified Kadomtsev–Petviashvili‐I equation. Using the long‐wave limit method, we derive both standard lump solutions and plane lump solutions from line‐soliton solutions. Through detailed asymptotic analysis, it is shown that standard lump solutions exhibit normal scattering. We further investigate lump chain solutions and identify elastic interactions with explicit phase shifts, as well as distinctive resonant patterns, including a characteristic “Y”‐shaped resonance and a unique parallel resonance phenomenon. An improved long ‐ wave limit approach is introduced to construct higher‐order lump solutions from lump chain solutions, yielding second‐order lump solutions, second‐order lump chain solutions, and semi‐rational soliton solutions. Notably, the second‐order lump solutions exhibit anomalous scattering, in which individual lumps propagate along curved trajectories despite sharing the same asymptotic velocity. Our analysis also establishes a connection between lump solutions and the root structure of Yablonskii–Vorob'ev polynomials. These results deepen the understanding of nonlinear wave interactions in (2 + 1)‐dimensional integrable systems.