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

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

Chaos, Solitons & Fractals, 2021, vol. 147, issue C

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.

Keywords: Ocean beaches and lakes; Shallow water waves; Boussinesq-Burgers system; Symbolic computation; Bäcklund transformations; Similarity reductions (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921002289

DOI: 10.1016/j.chaos.2021.110875

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