Solitary oscillations and multiple antikink-kink pairs in the double sine-Gordon model

Abstract

We study kink-antikink collisions in a particular case of the double sine-Gordon model depending on only one parameter $r$. The scattering process of large kink-antikink shows the changing of the topological sector. For some parameter intervals we observed two connected effects: the production of up to five antikink-kink pairs and up to three solitary oscillations. The scattering process for small kink-antikink has several possibilities: the changing of the topological sector, one-bounce collision, two-bounce collision, or formation of a bion state. In particular, we observed for small values of $r$ and velocities, the formation of false two-bounce windows and the suppression of true two-bounce windows, despite the presence of an internal shape mode.

25 pages, 36 figures, v2: significant extra material, new figures and references added

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• Wobbling kinks in a two-component scalar field theory: Interaction between shape modes
• Resonance mediated by fermions in kink-antikink collisions
• Kink scattering in the presence of geometric constrictions
• Vacuum state perturbed by an oscillon: composite configurations in ${\varphi }^4$ model