Abstract. We show that linear stability analysis not only describes the effect of modulation instability (MI) of a plane wave in nonlinear media but it also predicts significant wave amplification outside of the standard instability band. As an example, we consider the classic MI in the case of the nonlinear Schrödinger equation. However, similar amplification may take place in many other nonlinear media that admit modulation instability.

Key words: Nonlinear Schrödinger equation, modulation instability.