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- Katie L. Oliveras, Vishal Vasan, Bernard Deconinck, Diane Henderson
- SIAM Journal of Applied Mathematics
- 2012

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)

- Bernard Deconinck, Thomas Trogdon, Vishal Vasan
- SIAM Review
- 2014

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)

A new method due to Fokas for explicitly solving boundary-value problems for linear partial differential equations is extended to equations with mixed partial derivatives. The Benjamin-Bona-Mahony equation is used as an example: we consider the Robin problem for this equation posed both on the half line and on the finite interval. For specific cases of the… (More)

- Vishal Vasan, Bernard Deconinck
- Appl. Math. Lett.
- 2013

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- Vishal Vasan, Katie L. Oliveras
- Appl. Math. Lett.
- 2017

The inverse water wave problem of bathymetry detection is the problem of deducing the bottom topography of the seabed from measurements of the water wave surface. In this paper, we present a fully nonlinear method to address this problem. The method starts from the Euler water wave equations for inviscid irrotational fluid flow, without any approximation.… (More)

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