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

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-Backlund 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-Backlund 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.