Capillary freak waves in He-II as a manifestation of discrete wave turbulent regime

Two fundamental findings of the modern theory of wave turbulence are 1) existence of Kolmogorov-Zakharov power energy spectra (KZ-spectra) in $k$-space, \cite{zak2}, and 2) existence of ``gaps" in KZ-spectra corresponding to the resonance clustering, \cite{K06-1}. Accordingly, three wave turbulent regimes can be singled out - \emph{kinetic} (described by wave kinetic equations and KZ-spectra, in random phase approximation, \cite{ZLF92}); \emph{discrete} (described by a few dynamical systems, with coherent phases corresponding to resonance conditions, \cite{K09b}) and \emph{mesoscopic} (where kinetic and discrete evolution of the wave field coexist, \cite{zak4}). We present an explanation of freak waves appearance in capillary waves in He-II, \cite{ABKL09}, as a manifestation of discrete wave turbulent regime. Implications of these results for other wave systems are briefly discussed.