TY - JOUR

T1 - Resonant collisions between lumps and periodic solitons in the Kadomtsev-Petviashvili i equation

AU - Rao, Jiguang

AU - He, Jingsong

AU - Malomed, Boris A.

N1 - Publisher Copyright:
© 2022 Author(s).

PY - 2022/1/1

Y1 - 2022/1/1

N2 - 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 → -∞, but it suddenly emerges from the periodic soliton chain, keeping its amplitude and velocity constant as t → +∞; or it exists as t → -∞ and merges into the periodic chain, disappearing at t → +∞. 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.

AB - 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 → -∞, but it suddenly emerges from the periodic soliton chain, keeping its amplitude and velocity constant as t → +∞; or it exists as t → -∞ and merges into the periodic chain, disappearing at t → +∞. 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.

UR - http://www.scopus.com/inward/record.url?scp=85123475571&partnerID=8YFLogxK

U2 - 10.1063/5.0064304

DO - 10.1063/5.0064304

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AN - SCOPUS:85123475571

SN - 0022-2488

VL - 63

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 1

M1 - 013510

ER -