Thinking about the oceanic shallow water via a generalized Whitham-Broer-Kaup-Boussinesq-Kupershmidt system

Abstract

Currently, fluid mechanics has been paid attention to. Hereby, making use of symbolic computation, we investigate a generalized Whitham-Broer-Kaup-Boussinesq-Kupershmidt system describing, e.g., the dispersive long waves in the oceanic shallow water. As for, e.g., the horizontal velocity of the water wave and height of the deviation from the equilibrium position of the water, we work out (1) two sets of the hetero-Bäcklund transformations, each of which, from that system to a known linear partial differential equation, and (2) two sets of the similarity reductions, each of which, from that system to a known ordinary differential equation. Our hetero-Bäcklund transformations and similarity reductions depend on the coefficients in that system, as for, e.g., the oceanic shallow water.