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We consider in this paper the 'shallow-water/shallow-water' asymptotic model obtained in Choi and Camassa (1999 J. Fluid Mech. 396 1-36), Craig et al (2005 Commun. Pure. Appl. Math. 58 1587-641) (one-dimensional interface) and Bona et al (2008 J. Math. Pures Appl. 89 538-66) (two-dimensional interface) from the two-layer system with rigid lid, for the description of large amplitude internal waves at the interface of two layers of immiscible fluids of different densities. For one-dimensionaldoi:10.1088/0951-7715/23/2/003 fatcat:zmalgbgdpzew5j6lhqlosmgyui