Resonant collisions between lumps and periodic solitons in the Kadomtsev-Petviashvili I equation

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 -> -infinity. 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 -> -infinity, but it suddenly emerges from the periodic soliton chain, keeping its amplitude and velocity constant as t -> -infinity; or it exists as t -> -infinity; and merges into the periodic chain, disappearing at t -> -infinity. In the case of the fully resonant interaction, the lump is an instanton, which emerges from the periodic chain and then merges into another chain, keeping its identify for a short time. Thus, in the case of the fully resonant collisions, the lumps are completely localized in time as well as in two-dimensional space, and they are call rogue lumps.

Automated summary

The resonant collisions between lumps and periodic solitons of the Kadomtsev-Petviashvili I equation are investigated in detail. Two types of resonant collisions, partly resonant and fully resonant, cause the lumps to become localized in time as instantons. In the fully resonant collisions, the lumps are completely localized in both time and two-dimensional space and are referred to as rogue lumps.