Two component integrable systems modelling shallow water waves
By Rossen I. Ivanov. 2009
147 citations recorded by the source corpus.
In this contribution we describe the role of several two-component integrable systems in the classical problem of shallow water waves. The starting point in our derivation is the Euler equation for an incompressible fluid, the equation of mass conservation, the simplest bottom and surface conditions and the constant vorticity condition. The approximate model equations are generated by introduction of suitable scalings and by truncating asymptotic expansions of the quantities to appropriate order. The so obtained equations can be related to three different integrable systems: a two component generalization of the Camassa-Holm equation, the Zakharov-Ito system and the Kaup-Boussinesq system. The significance of the results is the inclusion of vorticity, an important feature of water waves that has been given increasing attention during the last decade. The presented investigation shows how -- up to a certain order -- the model equations relate to the shear flow upon which the wave resides. In particular, it shows exactly how the constant vorticity affects the equations.
Subfields: Oceanography, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/45be545227fae49006e6b705a25a820a7b493ad8
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In Oceanography
In Statistical and Nonlinear Physics
Citations in the corpus
- Wave Breaking and Global Existence for a Generalized Two-Component Camassa–Holm System (2010, methodology): “[20] A. Constantin and R.I. Ivanov, On an integrable two-component Camassa-Holm shallow water system, Phys.”