Instability and noise-induced thermalization of Fermi-Pasta-Ulam recurrence in the nonlinear Schrödinger 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 Schrödinger equation. The predicted initial stage of noise growth is in a good agreement with simulations, and is expected to provide further insight into the subsequent dynamics of the field evolution after recurrence breakup.