Compact kinks in a modified Christ-Lee model

TL;DR

This paper investigates compact kink solutions in a modified Christ-Lee model with non-analytic potentials, exploring their internal modes, collision dynamics, and unique phenomena like oscillon formation and false vacuum bubble creation.

Contribution

It introduces new compact kink solutions in a non-analytic potential framework and analyzes their collision behavior and internal modes, revealing novel dynamical phenomena.

Findings

Discovery of compact kinks with internal modes.

Observation of oscillon formation in high-velocity collisions.

Identification of false vacuum bubble formation during kink interactions.

Abstract

We study compact kinks in a modified Christ-Lee model where the potential is a non-analytic function at the minima. The model has two control parameters that determine the order of the potential and its overall shape. We consider cases in which the potential has a double well shape, a triple well shape, as well as cases with a false vacuum. Compact kink solutions and their internal modes are found for each of these cases. We also study the collision of such kinks and their dependence on the solitons velocity and on the potential parameters. Several interesting dynamical processes are reported, such as the formation of central oscillons for some high velocity collisions, absence of outgoing solitons in cases where the potential is given by piece-wise linear functions, and the decoupling of subkinks from the larger kink in cases with false vacuum, leading to the formation of false vacuum bubbles.