  In this work we present a further analytical development and a numerical
implementation of the recently suggested theoretical model for highly nonlinear
potential long-crested water waves, where weak three-dimensional effects are
included as small corrections to exact two-dimensional equations written in the
conformal variables [V.P. Ruban, Phys. Rev. E 71, 055303(R) (2005)]. Numerical
experiments based on this theory describe the spontaneous formation of a single
weakly three-dimensional large-amplitude wave (alternatively called freak,
killer, rogue or giant wave) on the deep water.
