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The modulational instability of waves in a medium under the action of anexternal monochromatic force and dissipation is considered. The model whichdescribes the nonlinear stage of the modulation instability was constructedwith using methods of so-called $S$-theory. Following this theory, we take intoaccount only interactions between modes with slowly varying relative phases.Within framework of this model, it is shown that the waves satisfying thecriterion of abnormality appears as a rule at the initial stage of theinstability. With further development of the process, the abnormal waves can bealso observed but their amplitudes decrease gradually with decreasing of theaverage wave height.

Extreme wave events at the initial stage of the modulational instability in a forced and damped wave medium