On hexagonal gravity water waves

In this paper we produce numerical, genuinely three-dimensional, hexagonal traveling wave solutions of the Euler equations for water waves using a surface integral formulation derived by Craig and Sulem. These calculations are free from the requirements of either long wavelength or two-dimensionality, both of which are crucial to the KdV and KP scaling regimes, and we produce hexagonal traveling waves of not only small but also moderate amplitude.