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Spinning Q-Balls for the Klein-Gordon-Maxwell Equations

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Abstract

The nonlinear Klein-Gordon-Maxwell equations provide models for the interaction between the electromagnetic field and matter. We assume that the nonlinear term W is positive and W(0) = 0. This fact makes the theory more suitable for physical models (for example models in supersymmetry theory and in cosmology; see e.g. [16, 22, 28] and their references).

A three dimensional vortex is a finite energy, stationary solution of the Klein-Gordon-Maxwell equations such that the matter field has nontrivial angular momentum and the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of three dimensional vortex-solutions.

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Authors and Affiliations

  1. Dipartimento di Matematica Applicata “U. Dini”, Università di Pisa, via F. Buonarroti 1/c, 56127, Pisa, Italy

    Vieri Benci

  2. Dipartimento di Matematica, Università di Bari and INFN sezione di Bari, Via Orabona 4, 70125, Bari, Italy

    Donato Fortunato

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  1. Vieri Benci
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  2. Donato Fortunato
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Correspondence to Donato Fortunato.

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Communicated by G. Gallavotti

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Benci, V., Fortunato, D. Spinning Q-Balls for the Klein-Gordon-Maxwell Equations. Commun. Math. Phys. 295, 639–668 (2010). https://doi.org/10.1007/s00220-010-0985-z

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