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Creation of weakly interacting lumps by degeneration of lump chains in the KP1 equation

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  • Zhang, Zhao
  • Guo, Qi
  • Stepanyants, Yury

Abstract

We present two different paths to degenerate normally interacting lump chains into anomalously interacting lump patterns within the Kadomtsev–Petviashvili (KP1) equation. In the first path, the periods of M lump chains with close velocities become infinite simultaneously; then, we obtain anomalously interacting M(M+1)/2 lumps directly in one step. The second path consists of two steps: firstly, M normally interacting lump chains degenerate into M anomalously interacting lump chains having the same parameters. Then, when the periods of anomalously interacting lump chains tend to infinity, we obtain M(M+1)/2 weakly interacting lumps. In the weakly interacting lump chains, the distance between them varies with time proportional to ln|t|.

Suggested Citation

  • Zhang, Zhao & Guo, Qi & Stepanyants, Yury, 2023. "Creation of weakly interacting lumps by degeneration of lump chains in the KP1 equation," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:chsofr:v:170:y:2023:i:c:s0960077923002990
    DOI: 10.1016/j.chaos.2023.113398
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