Resonant collisions of lump chains in the (2+1)-dimensional Yu-Toda-Sasa-Fukuyama equation

Abstract This paper investigates the resonant collisions between lump chains, as well as those between lump chains and a lump in the Yu-Toda-Sasa-Fukuyama equation, deepening the understanding of normal and resonant interactions in lump chains. The resonant collision of two lump chains can be categorized into two types: oblique collisions which resemble a Y-type structure, and parallel collisions which involve the fission or fusion of lump chains. The interaction between three lump chains exhibits greater complexity. Depending on whether all chains undergo resonance, the process is classified as either partial or complete resonance, with each type further divided into oblique and parallel collisions. The general resonance conditions for M lump chains are then established. Similarly, we analyze resonant collisions between a single lump and one or two lump chains, and derive resonance conditions for M lump chains interacting with a lump. We further complement our analysis of the dynamical behavior of lump chains under different resonance scenarios with graphical illustrations of their trajectories. The findings offer theoretical insights for applications in water wave dynamics, nonlinear optics, and related fields.