SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Fast and accurate computation of solitary waves to the free surface Euler equations

D. Dutykh and D. Clamond

Abstract
Among different kinds of special solutions, solitary waves play the central role in the nonlinear science. These solutions are very common in optics, plasma physics, but also in the hydrodynamics. In the present study we propose a fast and accurate numerical method to compute solitary wave solutions to the free surface Euler equations. It is based on the conformal mapping technique combined with an efficient Fourier-type pseudo-spectral method. The resulting nonlinear equation is solved using the Petviashvili iterative scheme. Our computational results are finally compared to some existing approaches such as the Tanaka method and the high order asymptotic expansion of Longuet-Higgins & Fenton (1974).

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