  In the framework of the focusing Nonlinear Schrodinger (NLS) equation we
study numerically the nonlinear stage of the modulation instability (MI) of the
condensate. As expected, the development of the MI leads to formation of
"integrable turbulence" [V.E. Zakharov, Turbulence in integrable systems, Stud.
in Appl. Math. 122, no. 3, 219-234, (2009)]. We study the time evolution of
it's major characteristics averaged across realizations of initial data - the
condensate solution seeded by small random noise with fixed statistical
properties. The measured quantities are: (1) wave-action spectrum and spatial
correlation function, (2) the probability density function (PDF) of wave
amplitudes and their momenta, and (3) kinetic and potential energies.
