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

TL;DR

This paper investigates kink-antikink collisions in the double sine-Gordon model, revealing complex phenomena such as multiple pair production, solitary oscillations, and varied scattering outcomes depending on the parameter and initial conditions.

Contribution

It provides new insights into the collision dynamics of the double sine-Gordon model, including the production of multiple pairs and oscillations, and the effects of the parameter r on scattering processes.

Findings

Up to five antikink-kink pairs produced

Observation of solitary oscillations

Changing of topological sectors during collisions

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.