A one-degree-of-freedom effective model for kink dynamics in a space-time dependent sine-Gordon system reproduces the stability boundaries of parametric resonance (Arnold tongues) seen in the full field model, with more complex dynamics appearing only near the lower edges of the tongues.
The korteweg–de vries equation
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Parametric Resonance in the Non-Autonomous Sine-Gordon Model
A one-degree-of-freedom effective model for kink dynamics in a space-time dependent sine-Gordon system reproduces the stability boundaries of parametric resonance (Arnold tongues) seen in the full field model, with more complex dynamics appearing only near the lower edges of the tongues.