Instability and noise-induced thermalization of Fermi-Pasta-Ulam recurrence in the nonlinear Schr\"odinger equation

We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi-Pasta-Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schr\"odinger equation. The predicted initial stage of noise growth is in good agreement with simulations, and is expected to provide further insight in the subsequent dynamics of the field evolution after recurrence breakup.