Breather dynamics in a stochastic sine-Gordon equation: evidence of noise-enhanced stability

TL;DR

This study investigates how stochastic noise influences the stability of sine-Gordon breathers, revealing that noise can unexpectedly prolong their lifespan through a phenomenon called noise-enhanced stability.

Contribution

It provides the first evidence that spatially-homogeneous noise can increase the stability and lifetime of sine-Gordon breathers in a dissipative and stochastic setting.

Findings

Noise can significantly extend breather lifetime.

Stability exhibits nonmonotonic dependence on noise intensity.

Results are robust against thermal background variations.

Abstract

The dynamics of sine-Gordon breathers is studied in the presence of dissipative and stochastic perturbations. Taking a stationary breather with a random phase value as the initial state, the performed simulations demonstrate that a spatially-homogeneous noisy source can make the oscillatory excitation more stable, i.e., it enables the latter to last significantly longer than it would in a noise-free scenario. Both the frequency domain and the localization of energy are examined to document the effectiveness of the noise-enhanced stability phenomenon, which emerges as a nonmonotonic behavior of an average characteristic time for the breather as a function of the noise intensity. The influence of the mode's starting frequency on the results and their robustness against an additional thermal background are also addressed.