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

• Published in: Qualitative theory of dynamical systems Vol. 23; no. 2
• Main Authors: Gao, Xin-Yi, Guo, Yong-Jiang, Shan, Wen-Rui
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.04.2024; Springer Nature B.V
• Subjects: Boussinesq equations; Difference and Functional Equations; Differential equations; Dynamical Systems and Ergodic Theory; Mathematics; Mathematics and Statistics; Shallow water; Similarity; Water waves; Ocean beaches; Hetero-Bäcklund transformation; Similarity reduction; Boussinesq-Burgers system; Shallow-water waves; Lakes; 70-XX; Computerized symbolic computation; 35-xx; 03Cxx; 68-04; 76-XX
• ISSN: 1575-5460; 1662-3592
• DOI: 10.1007/s12346-023-00905-w

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.