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BIRS Workshop Lecture Videos

Fully localised solitary gravity-capillary water waves Groves, Mark


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.

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