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

Abstract

• Water waves play an important role in the marine/offshore engineering, hydraulic engineering , etc. • For the water waves near an ocean beach or in a lake, we study a Boussinesq-Burgers system. • Look at water-wave horizontal velocity and height deviating from the equilibrium position of water. • Symbolic computation leads to two hetero-Backlund Transformations and a similarity reduction. • Our results rely on the oceanic water-wave dispersive power. 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.