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

TL;DR

This paper studies how noise grows and causes instability in the nonlinear Schrödinger equation during Fermi-Pasta-Ulam recurrence, combining stability analysis with numerical simulations.

Contribution

It introduces a Floquet linear stability analysis of periodic solutions to explain noise growth and recurrence breakup in the nonlinear Schrödinger equation.

Findings

Noise growth during modulation instability matches stability analysis predictions

Recurrence breakup is driven by noise-induced instability

Numerical simulations confirm theoretical predictions

Abstract

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.