On the Oceanic/Laky Shallow-Water Dynamics through a Boussinesq-Burgers System

• Xin-Yi Gao ^[2] ; Yong-Jiang Guo ^[1] ; Wen-Rui Shan ^[1]
  1. [1] Beijing University of Posts and Telecommunications

     Beijing University of Posts and Telecommunications

     China

     
  2. [2] North China University of Technology & Beijing University of Posts and Telecommunications
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 2, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Motivation/Development: In order to investigate the shallow-water waves, researchers have introduced many nice models, e.g., a Boussinesq-Burgers system for cetain shallow-water waves near an ocean beach/inside a lake, which we study here via computerized symbolic computation. Originality/Novelty with Potential Application:

    Concerning the height deviating from the equilibrium position of water as well as the field of horizontal velocity, we now construct a hetero-Bäcklund transformation coupling that system to a known partial differential system, as well as two sets of the similarity reductions, starting at that system towards a known ordinary differential equation. Both our hetero-Bäcklund transformation and similarity reductions lean upon the dispersive power in the shallow water. Results could help the further study on the oceanic/laky shallow-water dynamics.

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