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Our aim is to describe the derivation of shallow water model equations for the constant vorticity case and to demonstrate how these equations can be related to two integrable systems: a two component integrable generalization of the Camassa-Holm equation and the Kaup - Boussinesq system.
R. Ivanov, Two component integrable systems modelling shallow water waves, Oberwolfach reports, Volume 6, Issue 1, 2009, Wave Motion (pp. pp. 429–462).