Noise-enhanced stability of sine-Gordon breathers.

We study the dynamics of sine-Gordon (SG) breathers in the presence of lossy and stochastic perturbations. In a solely dissipative case, a breather radiatively decays within a time interval of the order of the inverse damping coefficient. Our simulations, for which the initial condition is a stationary breather with a random phase value, indicate that a spatially uniform noisy source can make this solitonic mode last much longer than it would in the noise-free scenario. Notably, we find a nonmonotonic behavior of an average characteristic time $vs.$ the noise intensity, which is a signature of the noise-enhanced stability effect. Both the frequency domain and the energy localization are examined to show the efficacy of the phenomenon. We also discuss the dependence of the results on the excitation's starting energy and their robustness against thermal fluctuations. This framework is useful for tackling the long-standing problem of the breather's detection in long Josephson junctions and its subsequent applications, $e.g.$, in information transmission and quantum computation. Lastly, SG breathers are also actively studied, $e.g.$, in cuprate superconductors, geology, and DNA systems.