A new look at the double sine-Gordon kink-antikink scattering

TL;DR

This paper investigates the scattering behavior of kink-antikink pairs in the double sine-Gordon model, revealing a critical velocity that determines whether they form bound states or pass through each other, along with novel oscillon phenomena.

Contribution

The study provides the first detailed numerical analysis of kink-antikink scattering in the double sine-Gordon model, highlighting a non-monotonous critical velocity dependence and discovering oscillon interactions.

Findings

Identification of a critical velocity $v_{cr}$ separating different scattering outcomes.

Observation of non-monotonous dependence of $v_{cr}$ on model parameter $R$.

Detection of oscillon formation and escape windows below $v_{cr}$.

Abstract

We study the kink-antikink scattering within the double sine-Gordon model. In the numerical simulations we found a critical value $v_{cr}$ of the initial velocity $v_{in}$, which separates two different scenarios: at $v_{in}<v_{cr}$ the kinks capture each other and form a bound state, while at $v_{in}>v_{cr}$ the kinks pass through each other and escape to infinities. We obtain non-monotonous dependence of $v_{cr}$ on the model parameter $R$. Besides that, at some initial velocities below $v_{cr}$ we observe formation and interaction of the so-called oscillons (new phenomenon), as well as escape windows (well-known phenomenon).