# American Institute of Mathematical Sciences

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Radial stability of periodic solutions of the Gylden-Meshcherskii-type problem
May  2015, 35(5): 1933-1968. doi: 10.3934/dcds.2015.35.1933

## Topological defects in the abelian Higgs model

 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, Canada

Received  December 2013 Revised  September 2014 Published  December 2014

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.
Citation: Magdalena Czubak, Robert L. Jerrard. Topological defects in the abelian Higgs model. Discrete & Continuous Dynamical Systems, 2015, 35 (5) : 1933-1968. doi: 10.3934/dcds.2015.35.1933
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