Multiple symmetry breaking induced by weak damping in the Fermi-Pasta-Ulam-Tsingou recurrence process

TL;DR

This paper demonstrates that weak damping can significantly alter the Fermi-Pasta-Ulam-Tsingou recurrence, causing multiple symmetry breakings through separatrix crossing, with experimental validation in fiber optics.

Contribution

It reveals how small dissipation influences recurrence symmetry in nonlinear systems and provides experimental evidence using fiber optics with tailored losses.

Findings

Weak damping causes multiple symmetry breakings in recurrence.

Separable crossing occurs at multiple critical attenuation values.

Experimental validation in fiber optics confirms theoretical predictions.

Abstract

We show that even small dissipation can strongly affect the Fermi-Pasta-Ulam-Tsingou recurrence phenomenon. Taking the fully nonlinear stage of modulational instability as an experimentally accessible example, we show that the linear attenuation induces the symmetry of the recurrence to be broken through separatrix crossing occurring at multiple critical values of the attenuation. We provide experimental evidence for this phenomenon in a fiber optics experiment designed in such a way that the effective losses can be carefully tailored by techniques based on Raman amplification.