Phase-pulling and breather instability in an AC-driven damped one- dimensional sine-Gordon system
An AC-driven damped sine-Gordon system, in the nonlinear Schrödinger regime, may converge into various nontrivial space-time attractors. One of them is breather riding on top of flat profile, both locked to the driver frequency. Using collective-coordinate ansatz for this attractor, and a multiple-scale perturbation technique, we study the location and nature of its instability. Among the various characteristics, this study includes understanding the role of the breather-background coupling, the structure of the associated unstable modes, the scaling structure of the instability boundary, etc. Most strikingly we find the instability mechanism and the above features to be strongly sensitive to the asymptotic phase-difference between the spatially localized breather and the spatially extended uniform background. We call this phenomenon ``phase-pulling''.
scientific article; zbMATH DE number 4011502