  We study numerically the integrable turbulence in the framework of the
focusing one-dimensional nonlinear Schrodinger equation using a new method --
the "growing of turbulence". We add to the equation a weak controlled pumping
term and start adiabatic evolution of turbulence from statistically homogeneous
Gaussian noise. After reaching a certain level of average intensity, we switch
off the pumping and realize that the "grown up" turbulence is statistically
stationary. We measure its Fourier spectrum, the probability density function
(PDF) of intensity and the autocorrelation of intensity. Additionally, we show
that, being adiabatic, our method produces stationary states of the integrable
turbulence for the intermediate moments of pumping as well. Presently, we
consider only the turbulence of relatively small level of nonlinearity;
however, even this "moderate" turbulence is characterized by enhanced
generation of rogue waves.
