  The classical theory of modulation instability (MI) attributed to
Bespalov-Talanov in optics and Benjamin-Feir for water waves is just a linear
approximation of nonlinear effects and has limitations that have been corrected
using the exact weakly nonlinear theory of wave propagation. We report results
of experiments in both, optics and hydrodynamics, which are in excellent
agreement with nonlinear theory. These observations clearly demonstrate that MI
has wider band of unstable frequencies than predicted by the linear stability
analysis. The range of areas where the nonlinear theory of MI can be applied is
actually much larger than considered here.
