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Resonant collisions among multi-breathers in the Mel’nikov system

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  • Xu, Yinshen
  • Li, Peixin
  • Mihalache, Dumitru
  • He, Jingsong

Abstract

We study the resonant collisions among multi-breathers in the Mel’nikov system, which is the Kadomtsev–Petviashvili (KP) equation coupled to the nonlinear Schrödinger equation. The two-breather resonant collisions are classified into two different types: (i) the emergence of a Y–shaped pattern when the breathers are oblique on each other; and (ii) the occurrence of fission of one breather into two breathers or fusion of two breathers into a single one when the involving breathers are parallel to each other. The resonant collision of three breathers generates more complicated collision scenarios. They are divided into separate and mutual resonant collisions depending on whether the whole breathers are involved in the collision process. On this basis, each collision mode demonstrates two distinct forms: (i) diverse web–shaped waveforms with three to five infinitely long breathers when three breathers are obliquely intersecting, where some waveforms display a polygonal pattern under certain parametric constraints; and (ii) the combination of plentiful fission or fusion processes when the breathers are parallel to each other. The parameter constraints are discussed in detail for the classification of resonant collision scenarios.

Suggested Citation

  • Xu, Yinshen & Li, Peixin & Mihalache, Dumitru & He, Jingsong, 2023. "Resonant collisions among multi-breathers in the Mel’nikov system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923003727
    DOI: 10.1016/j.chaos.2023.113471
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    References listed on IDEAS

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    1. Rao, Jiguang & Mihalache, Dumitru & He, Jingsong & Zhou, Fang, 2023. "Degenerate and non-degenerate vector solitons and their interactions in the two-component long-wave–short-wave model of Newell type," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Malomed, B.A., 2022. "Multidimensional dissipative solitons and solitary vortices," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    3. Yue-jun Deng & Rui-yu Jia & Ji Lin, 2019. "Lump and Mixed Rogue-Soliton Solutions of the (2 + 1)-Dimensional Mel’nikov System," Complexity, Hindawi, vol. 2019, pages 1-9, November.
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