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Shallow-water-wave studies on a (2 + 1)-dimensional Hirota–Satsuma–Ito system: X-type soliton, resonant Y-type soliton and hybrid solutions

Author

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  • Shen, Yuan
  • Tian, Bo
  • Zhou, Tian-Yu
  • Gao, Xiao-Tian

Abstract

Water waves can be seen in the rivers, lakes, oceans, etc. A (2 + 1)-dimensional Hirota–Satsuma–Ito system, which arises in the shallow water waves, is investigated in this work. Based on the given N-soliton solutions, we develop certain X-type and resonant Y-type soliton solutions via the Hirota method and symbolic computation, where N is a positive integer. We also construct some hybrid solutions consisting of the resonant Y-type solitons, solitons, breathers and lumps. The graphics we present show that the hybrid solutions consisting of the resonant Y-type solitons and solitons/breathers/lumps, respectively, describe the interactions between the resonant Y-type solitons and solitons/breathers/lumps. The obtained results are dependent on the water-wave coefficient in that system.

Suggested Citation

  • Shen, Yuan & Tian, Bo & Zhou, Tian-Yu & Gao, Xiao-Tian, 2022. "Shallow-water-wave studies on a (2 + 1)-dimensional Hirota–Satsuma–Ito system: X-type soliton, resonant Y-type soliton and hybrid solutions," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922000728
    DOI: 10.1016/j.chaos.2022.111861
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    Cited by:

    1. Li, Liu-Qing & Gao, Yi-Tian & Yu, Xin & Ding, Cui-Cui & Wang, Dong, 2022. "Bilinear form and nonlinear waves of a (1+1)-dimensional generalized Boussinesq equation for the gravity waves over water surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 494-508.
    2. Cao, Na & Yin, XiaoJun & Bai, ShuTing & LiYangXu,, 2023. "Breather wave, lump type and interaction solutions for a high dimensional evolution model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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