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

TL;DR

This study investigates how noise and ac forcing can induce and stabilize sine-Gordon breathers, revealing optimal noise levels for their formation and analyzing their statistical properties under different boundary conditions.

Contribution

It demonstrates the cooperative effect of noise and ac forcing in breather emergence, providing detailed statistical analysis and boundary condition effects, which is a novel insight in sine-Gordon dynamics.

Findings

Breather number increases with noise amplitude.

Breather spatial distribution depends on boundary conditions.

Optimal noise levels exist for breather generation.

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 (NBC and PBC, respectively), 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 NBC, whereas it is essentially uniform for PBC. 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 NBC (PBC).