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Beholding the shallow water waves near an ocean beach or in a lake via a Boussinesq-Burgers system

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

Abstract

Water waves, one of the most common phenomena in nature, play an important role in the marine/offshore engineering, hydraulic engineering, energy development, mechanical engineering, etc. Hereby, for the shallow water waves near an ocean beach or in a lake, we study a Boussinesq-Burgers system. With respect to the water-wave horizontal velocity and height deviating from the equilibrium position of water, we find out (1) two hetero-Bäcklund transformations via the Bell polynomials and symbolic computation, and (2) a set of the similarity reductions via symbolic computation, to a known ordinary differential equation, for which we also construct some solutions. The results rely on the oceanic water-wave dispersive power. We hope that our hetero-Bäcklund transformations and similarity reductions could help the researchers investigate certain modes of the shallow water waves near an ocean beach.

Suggested Citation

  • Gao, Xin-Yi & Guo, Yong-Jiang & Shan, Wen-Rui, 2021. "Beholding the shallow water waves near an ocean beach or in a lake via a Boussinesq-Burgers system," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921002289
    DOI: 10.1016/j.chaos.2021.110875
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    Cited by:

    1. Han, Peng-Fei & Zhang, Yi, 2024. "Investigation of shallow water waves near the coast or in lake environments via the KdV–Calogero–Bogoyavlenskii–Schiff equation," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    2. Kudryashov, Nikolay A., 2021. "Generalized Hermite polynomials for the Burgers hierarchy and point vortices," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    3. Yilong Li & Qiang Xu & Yujie Li & Yuanbei Li & Cong Liu, 2022. "Application of Microbial-Induced Calcium Carbonate Precipitation in Wave Erosion Protection of the Sandy Slope: An Experimental Study," Sustainability, MDPI, vol. 14(20), pages 1-16, October.

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