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By performing two parallel numerical experiments -- solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation -- we examined the applicability of the theory of weak turbulence to the description of the time evolution of an ensemble of free surface waves (a swell) on deep water. We observed qualitative coincidence of the results. To achieve quantitative coincidence, we augmented the kinetic equation by an empirical dissipation term modelling the strongly nonlineardoi:10.1103/physrevlett.99.164501 pmid:17995256 fatcat:k7dlhojhljfk3pg7om55b4hshy