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Variational Approach to Uniform Rigid Rotation of Ginzburg—Landau Vortices

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Abstract

Time periodic solutions for the hyperbolic gauged Ginzburg–Landau system, with spatial domain the unit disc, are shown to exist. Time periodic solutions representing bound states of vortices rotating about one another have been previously obtained in the near self-dual limit, using perturbative techniques. In contrast, we here take a variational approach, the solutions being obtained as critical points of an indefinite functional. We consider a special class of solutions which map out, uniformly in time, an orbit of the rotation group SO(2). It is shown that in the limit of large coupling constant the solutions have nontrivial time dependence or, as is shown to be equivalent, are not radially symmetric in any gauge.

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References

  1. Berger, M. and Chen, Y. Y.: Symmetric vortices for the Ginzburg-Landau equations of superconductivity and the nonlinear desingularization phenomenon, J. Funct. Anal. 82(2) (1989), 259–295.

    Google Scholar 

  2. Bethuel and Riviere, Vortices for a variational problem related to superconductivity, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995), 243–303.

    Google Scholar 

  3. Coron, J.: Periode minimale pour une corde vibrante de longeur infinie, C.R. Acad. Sci. A 294 (1982), 127–129.

    Google Scholar 

  4. Jaffe, A. and Taubes, C.: Vortices and Monopoles, Birkhäuser, Basel, 1982.

    Google Scholar 

  5. Montgomery, R.: unpublished notes.

  6. Piette, B., Schroers, B. and Zakrzewski, W. J.: Dynamics of baby skyrmions, Nuclear Phys. B 439(1–2) (1995), 205–235.

    Google Scholar 

  7. Plohr, B.: PhD thesis, Princeton, 1980.

  8. Pyke, R. and Sigal, I.: Nonlinear wave equations: constraints on periods and exponential bounds for periodic solutions, Duke Math. J. 88(1) (1997), 133–180.

    Google Scholar 

  9. Stuart, D.M. A.: Minimal periods for solutions of some classical field equations, SIAMJ. Math. Anal. 27(4) (1996), 1095–1101.

    Google Scholar 

  10. Stuart, D. M. A.: Periodic solutions of the Abelian Higgs model and rigid rotation of vortices, Geom. Funct. Anal. 9 (1999), 568–595.

    Google Scholar 

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, U.K.

    Sophia Demoulini

  2. Centre for Mathematical Sciences, University of Cambridge, Cambridge, U.K.

    David M. A. Stuart

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  1. Sophia Demoulini
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  2. David M. A. Stuart
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Demoulini, S., Stuart, D.M.A. Variational Approach to Uniform Rigid Rotation of Ginzburg—Landau Vortices. Letters in Mathematical Physics 52, 127–142 (2000). https://doi.org/10.1023/A:1007621017448

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  • DOI: https://doi.org/10.1023/A:1007621017448

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