  We study numerically the statistics of waves for generalized one-dimensional
Nonlinear Schrodinger (NLS) equation that takes into account focusing six-wave
interactions, dumping and pumping terms. We demonstrate the universal behavior
of this system for the region of parameters when six-wave interactions term
affects significantly only the largest waves. In particular, in the
statistically steady state of this system the probability density function
(PDF) of wave amplitudes turns out to be strongly non-Rayleigh one for large
waves, with characteristic "fat tail" decaying with amplitude $|\Psi|$ close to
$\propto\exp(-\gamma|\Psi|)$, where $\gamma>0$ is constant. The corresponding
non-Rayleigh addition to the PDF indicates strong intermittency, vanishes in
the absence of six-wave interactions, and increases with six-wave coupling
coefficient.
