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Fully localised solitary gravity-capillary water waves

Banff International Research Station for Mathematical Innovation and Discovery

We consider the classical gravity-capillary water-wave problem in its usual formulation as a three-dimensional free-boundary problem for the Euler equations for a perfect fluid. A <em>solitary wave</em> is a solution representing a wave which moves in a fixed direction with constant speed and without change of shape; it is <em>fully localised</em> if its profile decays to the undisturbed state of the water in every horizontal direction. The existence of fully localised solitary waves has been predicted on the basis of simpler model equations, namely the Kadomtsev-Petviashvili (KP) equation in the case of strong surface tension and the Davey-Stewartson (DS) system in the case of weak surface tension. In this talk we confirm the existence of such waves as solutions to the full water-wave problem and give rigorous justification for the use of the model equations. This is joint work with Boris Buffoni and Erik Wahlen.

Mathematics; Fluid mechanics; Partial differential equations; Fluid dynamics

video/mp4

Author affiliation: Saarland University

2017-05-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61514

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/