  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.
