Three-dimensional Localized Solitary Gravity-Capillary Waves

Abstract

In a weakly nonlinear model equation for capillary-gravity water waves on a two-dimensional free surface, we show, numerically, that there exist localized solitary traveling waves for a range of parameters spanning from the long wave limit (with Bond number B>1/3, in the regime of the Kadomtsev-Petviashvilli-I equation) to the wavepacket limit (B>1/3, in the Davey-Stewartson regime). In fact, we show that these two regimes are connected with a single continuous solution branch of nonlinear localized solitary solutions crossing B=1/3.