Wave amplification outside of the modulation instability band

We show that linear stability analysis not only describes the effect of modulation instability 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 Schro center dot dinger equation. However, similar amplification may take place in many other nonlinear media that admit modulation instability.