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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.
To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability (MI) from non-instantaneous nonlinearities in photorefractive crystals. With a temp
Instabilities are common phenomena frequently observed in nature, sometimes leading to unexpected catastrophes and disasters in seemingly normal conditions. The simplest form of instability in a distributed system is its response to a harmonic modula
We present both theoretical description and experimental observation of the modulation instability process and related rogue breathers in the case of stationary periodic background waves, namely cnoidal and dnoidal envelopes. Despite being well-known
The nonlinear stage of modulational instability in optical fibers induced by a wide and easily accessible class of localized perturbations is studied using the nonlinear Schrodinger equation. It is showed that the development of associated spatio-tem
We report an exact link between Zakharov-Gelash super-regular (SR) breathers (formed by a pair of quasi-Akhmediev breathers) with interesting different nonlinear propagation characteristics and modulation instability (MI). This shows that the absolut