Noise-induced, ac-stabilized sine-Gordon breathers: Emergence and statistics

Abstract

Noisy and ac forcing can cooperatively lead to the emergence of sine-Gordon breathers robust to dissipation. This phenomenon is studied, for both Neumann and periodic boundary conditions, at different values of the main system parameters, such as the noise intensity and the ac frequency-amplitude pair. In all the considered cases, nonmonotonicities of the probability of generating only breathers versus the noise strength are observed, implying that optimal noise ranges for the breather formation process exist. Within the latter scenarios, the statistics of the breathers’ number, position, and amplitude are analyzed. The number of breathers is found to grow, on average, with the noise amplitude. The breathers’ spatial distribution is sharply peaked at the system’s edges for Neumann boundary conditions, whereas it is essentially uniform for periodic boundary conditions. The average breather amplitude is dictated by the ac frequency-amplitude pair. Finally, a size analysis shows that the minimum system length for the generation mechanism is given by the typical breather half-width (width) in the case of Neumann boundary conditions (periodic boundary conditions).