Parametric Resonance in the Non-Autonomous Sine-Gordon Model
arXiv:2507.17837 · doi:10.1063/5.0296470
Abstract
The sine-Gordon model is studied with model parameters that depend on both space and time. An effective model with one degree of freedom is constructed, allowing the description of the kink movement in both a temporally non-autonomous and spatially inhomogeneous setting. As a highly demanding test of the reduced model, the case of a temporal drive leading to a parametric instability is considered. Here, the boundaries of the instability region in the form of Arnold tongues were examined in both the simplified effective model and the full field model. Good agreement was obtained as concerns the regions of stability. It was observed that only in the bottom parts of Arnold's tongues is the dynamics of the field model more complicated than in the approximate model.
12 pages, 8 figures
References in corpus (14)
- Feshbach Resonances in Ultracold Gases
- Temporal tweezing of light: trapping and manipulation of temporal cavity solitons
- Extended parametric resonances in nonlinear Schrodinger systems
- Excitations of a Superfluid in a 3D Optical Lattice
- Faraday waves in Bose-Einstein condensates
- Dynamical Stability of a Many-body Kapitza Pendulum
- Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals
- Detecting phonons and persistent currents in toroidal Bose-Einstein condensates by means of pattern formation
- Parametric excitation of a Bose-Einstein condensate in a 1D optical lattice
- Stability diagram and growth rate of parametric resonances in Bose-Einstein condensates in one-dimensional optical lattices
- Spontaneous Formation of Star-Shaped Surface Patterns in a Driven Bose-Einstein Condensate
- Observation of supersolid-like sound modes in a driven quantum gas
- Double sine-Gordon class of universal coarsening dynamics in a spin-1 Bose gas
- Kink movement on a periodic background