  We perform full-scale numerical simulation of instability of weakly nonlinear
waves on the surface of deep fluid. We show that the instability development
leads to chaotization and formation of wave turbulence.
  We study instability both of propagating and standing waves. We studied
separately pure capillary wave unstable due to three-wave interactions and pure
gravity waves unstable due to four-wave interactions. The theoretical
description of instabilities in all cases is included into the article. The
numerical algorithm used in these and many other previous simulations performed
by authors is described in details.
