  Irregular waves which experience the time-limited external forcing within the
framework of the nonlinear Schrodinger (NLS) equation are studied numerically.
It is shown that the adiabatically slow pumping (the time scale of forcing is
much longer than the nonlinear time scale) results in selective enhancement of
the solitary part of the wave ensemble. The slow forcing provides eventually
wider wavenumber spectra, larger values of kurtosis and higher probability of
large waves. In the opposite case of rapid forcing the nonlinear waves readjust
passing through the stage of fast surges of statistical characteristics. Single
forced envelope solitons are considered with the purpose to better identify the
role of coherent wave groups. An approximate description on the basis of
solutions of the integrable NLS equation is provided. Applicability of the
Benjamin - Feir Index to forecasting of conditions favourable for rogue waves
is discussed.
