Modulation instability of waves driven by external source in dumped medium

In present paper we study the dynamics of modulation instability of waves in dumped medium in presence of an external monochromatic source. The instability of intensive gravitation wave on the oceanic surface is considered. It is shown that under condition of small ratio of side mode amplitudes to the central wave amplitude it is possible to take into account the interaction of the side modes with the central mode only. The appearance of the enormous waves of large amplitude is typical for the initial stage of modulation instability. During the latter dynamics the appearance of waves satisfying the anomaly criterion can also be revealed, but their amplitudes gradually diminish as well as the average choppiness amplitude.