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A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the surface elevation which is obtained from the Euler formulation of the water-wave problem without approximation. From this… (More)

The classical methods for solving initial-boundary-value problems for linear partial differential equations with constant coefficients rely on separation of variables, and specific integral transforms. As such, they are limited to specific equations, with special boundary conditions. Here we review a method introduced by Fokas, which contains the classical… (More)

The Bernoulli boundary condition for traveling water waves is obtained from Euler's equation for inviscid flow by employing two key reductions: (i) the traveling wave assumption, (ii) the introduction of a velocity potential. Depending on the order of these reductions, the Bernoulli boundary condition may or may not contain an arbitrary constant. This note… (More)

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