A shadowing lemma for abelian Higgs vortices

2004/12/01 by Marta Macri', Macri', Marta, Margherita Nolasco +3
Mathematics · Physics and Astronomy · #35J60 (primary) #58E15 #81T13 (secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35J60 #msc:58E15 #msc:81T13

paper · pdf · doi:10.48550/arxiv.math/0412025

18 pages

arxiv created 2004/12/01 · arxiv updated 2009/12/01

Abstract

We use a shadowing-type lemma in order to analyze the singular, semilinear elliptic equation describing static self-dual abelian Higgs vortices. Such an approach allows us to construct new solutions having an infinite number of arbitrarily prescribed vortex points. Furthermore, we obtain the precise asymptotic profile of the solutions in the form of an approximate superposition rule, up to an error which is exponentially small.

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