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Topological defects in the abelian Higgs model. (English) Zbl 1310.35169

Summary: 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.

MSC:

35L70 Second-order nonlinear hyperbolic equations
49Q05 Minimal surfaces and optimization
35Q85 PDEs in connection with astronomy and astrophysics
35B40 Asymptotic behavior of solutions to PDEs
81T13 Yang-Mills and other gauge theories in quantum field theory
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