Oscillons and oscillating kinks in the Abelian-Higgs model

TL;DR

This paper investigates the classical dynamics of the Abelian Higgs model, deriving effective equations to predict and analyze the existence and stability of oscillons and kinks, supported by numerical simulations.

Contribution

It introduces an asymptotic multiscale expansion method to derive effective equations, predicting oscillons and kinks, and compares these with numerical results.

Findings

Oscillons are stable and spontaneously form via modulational instability.

Kinks are found to be unstable in the studied regimes.

Numerical simulations agree well with analytical predictions.

Abstract

We study the classical dynamics of the Abelian Higgs model employing an asymptotic multiscale expansion method, which uses the ratio of the Higgs to the gauge field amplitudes as a small parameter. We derive an effective nonlinear Schr\"{o}dinger equation for the gauge field, and a linear equation for the scalar field containing the gauge field as a nonlinear source. This equation is used to predict the existence of oscillons and oscillating kinks for certain regimes of the ratio of the Higgs to the gauge field masses. Results of numerical simulations are found to be in very good agreement with the analytical findings, and show that the oscillons are robust, while kinks are unstable. It is also demonstrated that oscillons emerge spontaneously as a result of the onset of the modulational instability of plane wave solutions of the model. Connections of the obtained solutions with the phenomenology of superconductors is discussed.