Efficient computation of steady solitary gravity waves

Denys Dutykh, Didier Clamond

Published 2013-02-07, updated 2013-05-23Version 2

An efficient numerical method to compute solitary wave solutions to the free surface Euler equations is reported. It is based on the conformal mapping technique combined with an efficient Fourier pseudo-spectral method. The resulting nonlinear equation is solved via the Petviashvili iterative scheme. The computational results are compared to some existing approaches, such as the Tanaka method and Fenton's high-order asymptotic expansion. Several important integral quantities are numerically computed for a large range of amplitudes. The integral representation of the velocity and acceleration fields in the bulk of the fluid is also provided.