Suppression of Modulation Instability by spatio-temporal modulation

Modulation Instability (MI) is at the basis of spontaneous pattern formation in many nonlinear spatially extended systems in Nature, technologies, and in everyday live. In spite of variety of spatial patterns in different systems, the very onset of a spatio-temporal dynamics, the breaking of initial spatial and temporal symmetry, is initiated by MI. The said is valid for dissipative nonlinear systems, where dissipative patterns set in, but also for conservative systems. The examples in latter case ranges from the filamentation of light in Kerr-nonlinear media, instabilities of Bose condensates with attractive interactions, to perhaps, the recently much discussed formation of the “rogue waves”.