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

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-Backlund 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-Backlund transformations and similarity reductions could help the researchers investigate certain modes of the shallow water waves near an ocean beach. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

In this study, we focused on shallow water waves near an ocean beach or in a lake, and discovered two hetero-Backlund transformations and a set of similarity reductions through the Bell polynomials and symbolic computation. These findings provide solutions to a known ordinary differential equation, based on the dispersive power of oceanic water waves, aiming to assist researchers in exploring certain modes of shallow water waves.