Rigorous derivation of dispersive boundary-layer models from full water-wave equations

Establish the rigorous derivation, from the full water-wave equations, of shallow-water or dispersive transmission models that include localized dispersive boundary layers near discontinuous bathymetries.

Background

Existing works cited in the paper derive or analyze shallow-water and dispersive transmission models with localized boundary layers by taking the reduced models as their starting point. The unresolved issue identified by the authors is to justify these reduced models directly from the full water-wave equations, including the emergence and structure of the boundary layer. The present paper addresses this question for linear water waves over a sharp step and derives a boundary-layer correction in a small-step regime, but the broader derivation problem remains open.