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Regarding the shallow water in an ocean via a Whitham-Broer-Kaup-like system: hetero-Bäcklund transformations, bilinear forms and M solitons

Author

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  • Gao, Xin-Yi
  • Guo, Yong-Jiang
  • Shan, Wen-Rui

Abstract

Considering the water waves, people have investigated many systems. In this paper, what we study is a Whitham-Broer-Kaup-like system for the dispersive long waves in the shallow water in an ocean. With respect to the water-wave horizontal velocity and deviation height from the equilibrium of the water, we construct (A) two branches of the hetero-Bäcklund transformations, from that system to a known constant-coefficient nonlinear dispersive-wave system, (B) two branches of the bilinear forms and (C) two branches of the M-soliton solutions, with M as a positive integer. Results rely upon the oceanic shallow-water coefficients in that system.

Suggested Citation

  • Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2022. "Regarding the shallow water in an ocean via a Whitham-Broer-Kaup-like system: hetero-Bäcklund transformations, bilinear forms and M solitons," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006944
    DOI: 10.1016/j.chaos.2022.112486
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    Citations

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    Cited by:

    1. Singh, Sudhir & Sakkaravarthi, K. & Murugesan, K., 2023. "Lump and soliton on certain spatially-varying backgrounds for an integrable (3+1) dimensional fifth-order nonlinear oceanic wave model," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. 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).
    3. Li, Lingfei & Zhu, Minting & Zheng, Han & Xie, Yingying, 2023. "Non-compatible partially PT symmetric Davey–Stewartson system: Rational and semi-rational solution with nonzero background," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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