Ocean shallow-water studies on a generalized Boussinesq-Broer-Kaup-Whitham system: Painlevé analysis and similarity reductions

Abstract

Today, shallow seas are the focus of scientists and explorers. We look into a generalized Boussinesq-Broer-Kaup-Whitham system, which describes certain gravity water waves in a shallow ocean scenario in terms of the wave height and surface velocity of the water wave, by proving that the system is Painlevé integrable and constructing two families of similarity reductions. Each family results in a well-studied ordinary differential equation that depends on the coefficients in the system.