Topological defects in the abelian Higgs model

Magdalena Czubak; Robert L. Jerrard

doi:10.3934/dcds.2015.35.1933

Article Contents

2015, Volume 35, Issue 5: 1933-1968. Doi: 10.3934/dcds.2015.35.1933

This issue Previous Article Radial stability of periodic solutions of the Gylden-Meshcherskii-type problem Next Article Integrability of potentials of degree $k \neq \pm 2$. Second order variational equations between Kolchin solvability and Abelianity

Topological defects in the abelian Higgs model

Magdalena Czubak^1, and
Robert L. Jerrard^2,

1.
Department of Mathematical Sciences, Binghamton University (SUNY), Binghamton, NY 13902-6000
2.
Department of Mathematics, University of Toronto, Bahen Centre 40 St. George St., Room 6290, Toronto, ON M5S 2E4

Received: December 2013

Revised: September 2014

Published: May 2017

Abstract / Introduction Related Papers Cited by

Abstract

We give a rigorous description of the dynamics of the Nielsen-Olesen vortex line. In particular, given a worldsheet of a string, we construct initial data such that the corresponding solution of the abelian Higgs model will concentrate near the evolution of the string. Moreover, the constructed solution stays close to the Nielsen-Olesen vortex solution.

Keywords:

Mathematics Subject Classification: Primary: 35L70, 49Q05; Secondary: 35Q85, 35B40.

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