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A shadowing lemma for abelian Higgs vortices

Marta Macri'·Margherita Nolasco·Tonia Ricciardi
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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 \textit{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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Marta Macri', Margherita Nolasco, Tonia Ricciardi. 2004-12-01. A shadowing lemma for abelian Higgs vortices. https://arxiv.org/abs/math/0412025

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