Figure shows the evolution of the spectral components in the modulation instability. Initially, all the energy is concentrated in the central mode (or frequency component). We can also see two weak seeding modes (sidebands) on either side of the central mode. During evolution, energy flows from the central mode into the higher-order modes. At the same time, the energy in the central mode decreases. An infinite number of modes become excited (we can show only three of them on each side). This happens until a certain point is reached where the energy flow starts to return from the higher modes back into the central component. This reciprocal energy exchange process between the pump and an infinite number of sidebands is nothing but the spectral manifestation of the Fermi-Pasta-Ulam recurrence phenomenon.

Akhmediev N. N. and Korneev V. I., Modulation Instability and periodic solutions of nonlinear Schrodinger equation, Theor. Math. Phys., 69, 1089 (1986).

Akhmediev N. N., Deja vu in optics, Nature, 413, No 6853, pp. 267-268 (2001).