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In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume the thickness of the upper and lower fluids to be of comparable size, and small compared to the characteristic… (More)

We study one-dimensional scattering for a decaying potential with rapid periodic oscillations and strong localized singularities. In particular, we consider the Schrödinger equation Hǫ ψ ≡ ` −∂ 2 x + V 0 (x) + q (x, x/ǫ) ´ ψ = k 2 ψ ± outgoing as |x| → ∞. We derive their ǫ small asymptotic behavior, from which the asymptotic behavior of scattering… (More)

The rigid-lid approximation is a commonly used simplification in the study of density-stratified fluids in oceanography. Roughly speaking, one assumes that the displacements of the surface are negligible compared with interface displacements. We offer a rigorous justification of this approximation in the case of two shallow layers of immiscible fluids with… (More)

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