Nonlinear three-dimensional gravity–capillary solitary waves

Abstract

Steady three-dimensional fully nonlinear gravity–capillary solitary waves are calculated numerically in infinite depth. These waves have decaying oscillations in the direction of propagation and monotone decay perpendicular to the direction of propagation. They travel at a velocity $U$ smaller than the minimum velocity $c_{min}$ of linear gravity–capillary waves. It is shown that the structure of the solutions in three dimensions is similar to that found by Vanden-Broeck & Dias (J. Fluid Mech. vol. 240, 1992, pp. 549–557) for the corresponding two-dimensional problem.