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

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 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 illustrate the effectiveness of the noise-enhanced stability phenomenon, which manifests itself as a nonmonotonic behavior of the mean first-passage time for the breather as a function of the noise intensity. The influence of the mode's initial frequency on the results and their robustness against an additional thermal background are also addressed. Overall, the analysis highlights a counter-intuitive, positive role of noise in the breather's persistence.