Resonant collisions of lumps with periodic solitons of the Kadomtsev–Petviashvili I equation
are investigated in detail. The usual lump is a stable weakly localized two-dimensional
soliton, which keeps its shape and velocity in the course of the evolution from t→−∞ to
t→+∞. However, the lumps would become localized in time as instantons, as a result of two
types of resonant collisions with spatially periodic (quasi-1D) soliton chains. These are partly
resonant and fully resonant collisions. In the former case, the lump does not exist at t→−∞ …