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Uniqueness of selfdual periodic Chern–Simons vortices of topological-type

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Abstract

In analogy with the abelian Maxwell–Higgs model (cf. Jaffe and Taubes in Vortices and monopoles, 1980) we prove that periodic topological-type selfdual vortex-solutions for the Chern–Simons model of Jackiw–Weinberg [Phys Rev Lett 64:2334–2337, 1990] and Hong et al. Phys Rev Lett 64:2230–2233, 1990 are uniquely determined by the location of their vortex points, when the Chern–Simons coupling parameter is sufficiently small. This result follows by a uniqueness and uniform invertibility property established for a related elliptic problem (see Theorem 3.6 and 3.7).

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  1. Dipartimento di Matematica, Universitá di Roma “Tor Vergata”, Via della Ricerca Scientifica, 00133, Roma, Italy

    Gabriella Tarantello

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  1. Gabriella Tarantello
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Correspondence to Gabriella Tarantello.

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Research supported by M.I.U.R. project: Variational Methods and Nonlinear Differential Equations.

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Tarantello, G. Uniqueness of selfdual periodic Chern–Simons vortices of topological-type. Calc. Var. 29, 191–217 (2007). https://doi.org/10.1007/s00526-006-0062-9

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