Wobbling double sine-Gordon kinks

TL;DR

This paper investigates the complex collision dynamics of kinks and antikinks in the double sine-Gordon model, revealing how vibrational modes influence resonance windows, energy transfer, and wobbling behavior.

Contribution

It introduces a detailed analysis of wobbling double sine-Gordon kinks, including the effects of vibrational modes on resonance structures and energy transfer during collisions.

Findings

Resonance windows exist only within a limited parameter range despite vibrational modes.

Excited vibrational modes can convert into translational energy, affecting collision outcomes.

The maximum energy density remains smooth within resonance windows.

Abstract

We study the collision of a kink and an antikink in the double sine-Gordon model with and without the excited vibrational mode. In the latter case, we find that there is a limited range of the parameters where the resonance windows exist, despite the existence of a vibrational mode. Still, when the vibrational mode is initially excited, its energy can turn into translational energy after the collision. This creates one-bounce as well as a rich structure of higher-bounce resonance windows that depend on the wobbling phase being in or out of phase at the collision and the wobbling amplitude being sufficiently large. When the vibrational mode is excited, the modified structure of one-bounce windows is observed in the whole range of the model's parameters, and the resonant interval with higher-bounce windows gradually increases with the wobbling amplitude. We estimated the center of the one-bounce windows using a simple analytical approximation for the wobbling evolution. The kinks' final wobbling frequency is Lorentz contracted, which is simply derived from our equations. We also report that the maximum energy density value always has a smooth behavior in the resonance windows.