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Consider a two-dimensional stratified solitary wave propagating through abody of water that is bounded below by an impermeable ocean bed. In this work,we study how such a wave can be reconstructed from data consisting of the wavespeed, upstream and downstream density profile, and the trace of the pressureon the bed. First, we prove that this data uniquely determines the wave, bothin the (real) analytic and Sobolev regimes. Second, for waves that consist ofmultiple layers of constant density immiscible fluids, we provide an exactformula describing each of the interfaces in terms of the data. Finally, forcontinuously stratified fluids, we detail a reconstruction scheme based onapproximation by layer-wise constant density flows.

Reconstruction of stratified steady water waves from pressure readings on the ocean bed