Scattering of the double sine-Gordon kinks

TL;DR

This paper investigates the scattering behavior of kinks and antikinks in the double sine-Gordon model, revealing a critical velocity that separates reflection from complex interactions, including capture, escape windows, and oscillon formation.

Contribution

It provides the first detailed analysis of the critical velocity dependence on model parameters and reports new phenomena like oscillon escape and bound states.

Findings

Critical velocity $v_{cr}$ depends on model parameters with multiple local maxima.

Below $v_{cr}$, oscillons can escape or form bound states.

New phenomena of oscillon escape and bound states are observed.

Abstract

We study the scattering of kink and antikink of the double sine-Gordon model. There is a critical value of the initial velocity $v_{cr}$ of the colliding kinks, which separates different regimes of the collision. At $v_{in}>v_{cr}$ we observe kinks reflection, while at $v_{in}<v_{cr}$ their interaction is complicated with capture and escape windows. We obtain the dependence of $v_{cr}$ on the parameter of the model. This dependence possesses a series of local maxima, which has not been reported by other authors. At some initial velocities below the critical value we observe a new phenomenon -- the escape of two oscillons in the final state. Besides that, at $v_{in}<v_{cr}$ we found the initial kinks' velocities at which the oscillons do not escape, and the final configuration looks like a bound state of two oscillons.