  The purpose of this article is numerical verification of the theory of weak
turbulence. We performed numerical simulation of an ensemble of nonlinearly
interacting free gravity waves (swell) by two different methods: solution of
primordial dynamical equations describing potential flow of the ideal fluid
with a free surface and, solution of the kinetic Hasselmann equation,
describing the wave ensemble in the framework of the theory of weak turbulence.
  In both cases we observed effects predicted by this theory: frequency
downshift, angular spreading and formation of Zakharov-Filonenko spectrum
$I_{\omega} \sim \omega^{-4}$. To achieve quantitative coincidence of the
results obtained by different methods, one has to supply the Hasselmann kinetic
equation by an empirical dissipation term $S_{diss}$ modeling the coherent
effects of white-capping. Using of the standard dissipation terms from
operational wave predicting model ({\it WAM}) leads to significant improvement
on short times, but not resolve the discrepancy completely, leaving the
question about optimal choice of $S_{diss}$ open. In a long run {\it WAM}
dissipative terms overestimate dissipation essentially.
