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All issues Volume 8 / No 5 (2013) Math. Model. Nat. Phenom., 8 5 (2013) 190-205 References
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Issue
Math. Model. Nat. Phenom.
Volume 8, Number 5, 2013
Bifurcations
Page(s) 190 - 205
DOI https://doi.org/10.1051/mmnp/20138512
Published online 17 September 2013
  1. A. A. Abrikosov. On the magnetic properties of superconductors of the second group. J. Explt. Theoret. Phys. (USSR) 32 (1957), 1147–1182. [Google Scholar]
  2. A. Aftalion, X. Blanc, F. Nier. Lowest Landau level functional and Bargmann spaces for Bose-Einstein condensates. J. Funct. Anal. 241 (2006), 661–702. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Aftalion, S. Serfaty. Lowest Landau level approach in superconductivity for the Abrikosov lattice close to Hc2. Selecta Math. (N.S.) 13 (2007), 183–202. [CrossRef] [MathSciNet] [Google Scholar]
  4. L. V. Alfors. Complex analysis. McGraw-Hill, New York, 1979. [Google Scholar]
  5. Y. Almog. On the bifurcation and stability of periodic solutions of the Ginzburg-Landau equations in the plane. SIAM J. Appl. Math. 61 (2000), 149–171. [CrossRef] [Google Scholar]
  6. Y. Almog, Abrikosov lattices in finite domains. Commun. Math. Phys. 262 (2006), 677-702. [Google Scholar]
  7. A. Ambrosetti, G. Prodi. A Primer of Nonlinear Analysis. Cambridge University Press, Cambridge, 1993. [Google Scholar]
  8. E. Barany, M. Golubitsky, J. Turski. Bifurcations with local gauge symmetries in the Ginzburg-Landau equations. Phys. D 56 (1992), 36–56. [CrossRef] [MathSciNet] [Google Scholar]
  9. M.S. Berger, Y. Y. Chen. Symmetric vortices for the nonlinear Ginzburg-Landau equations of superconductivity, and the nonlinear desingularization phenomenon. J. Fun. Anal. 82 (1989) 259-295. [CrossRef] [Google Scholar]
  10. S. J. Chapman. Nucleation of superconductivity in decreasing fields. European J. Appl. Math. 5 (1994), 449–468. [MathSciNet] [Google Scholar]
  11. S. J. Chapman, S. D. Howison, J. R. Ockedon. Macroscopic models of superconductivity. SIAM Rev. 34 (1992), 529–560. [CrossRef] [MathSciNet] [Google Scholar]
  12. Q. Du, M. D. Gunzburger, J. S. Peterson. Analysis and approximation of the Ginzburg-Landau model of superconductivity. SIAM Rev. 34 (1992), 54–81. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Dutour. Phase diagram for Abrikosov lattice. J. Math. Phys. 42 (2001), 4915–4926. [CrossRef] [Google Scholar]
  14. M. Dutour. Bifurcation vers l’état d’Abrikosov et diagramme des phases. Thesis Orsay, http://www.arxiv.org/abs/math-ph/9912011. [Google Scholar]
  15. G. Eilenberger, Zu Abrikosovs Theorie der periodischen Lösungen der GL-Gleichungen für Supraleiter 2. Z. Physik 180 (1964), 32–42. [Google Scholar]
  16. S. Fournais, B. Helffer. Spectral Methods in Surface Superconductivity. Progress in Nonlinear Differential Equations and their Applications, vol. 77, Birkhäuser, 2010. [Google Scholar]
  17. S. Gustafson, I.M. Sigal. The stability of magnetic vortices. Comm. Math. Phys. 212 (2000) 257-275. [CrossRef] [MathSciNet] [Google Scholar]
  18. S. Gustafson, I. M. Sigal. Mathematical Concepts of Quantum Mechanics. Springer, 2006. [Google Scholar]
  19. S. J. Gustafson, I. M. Sigal, T. Tzaneteas. Statics and dynamics of magnetic vortices and of Nielsen-Olesen (Nambu) strings. J. Math. Phys. 51, 015217 (2010). [CrossRef] [Google Scholar]
  20. A. Jaffe, C. Taubes. Vortices and Monopoles: Structure of Static Gauge Theories. Progress in Physics 2. Birkhäuser, Boston, Basel, Stuttgart, 1980. [Google Scholar]
  21. W.H. Kleiner, L. M. Roth, S. H. Autler. Bulk solution of Ginzburg-Landau equations for type II superconductors: upper critical field region. Phys. Rev. 133 (1964), A1226–A1227. [CrossRef] [Google Scholar]
  22. G. Lasher. Series solution of the Ginzburg-Landau equations for the Abrikosov mixed state. Phys. Rev. 140 (1965), A523–A528. [CrossRef] [Google Scholar]
  23. S. Nonnenmacher, A. Voros. Chaotic eigenfunctions in phase space. J. Statist. Phys. 92 (1998), 431–518. [CrossRef] [MathSciNet] [Google Scholar]
  24. F. Odeh, Existence and bifurcation theorems for the Ginzburg-Landau equations. J. Math. Phys. 8 (1967), 2351–2356. [CrossRef] [Google Scholar]
  25. Yu. N. Ovchinnikov. Structure of the supercponducting state near the critical fiel Hc2 for values of the Ginzburg-Landau parameter κ close to unity. JETP. 85 (4) (1997), 818–823. [CrossRef] [Google Scholar]
  26. J. Rubinstein. Six Lectures on Superconductivity. Boundaries, interfaces, and transitions (Banff, AB, 1995), 163–184, CRM Proc. Lecture Notes, 13, Amer. Math. Soc., Providence, RI, 1998. [Google Scholar]
  27. E. Sandier, S. Serfaty. Vortices in the Magnetic Ginzburg-Landau Model. Progress in Nonlinear Differential Equations and their Applications, vol.l 70, Birkhäuser, 2007. [Google Scholar]
  28. P. Takáč. Bifurcations and vortex formation in the Ginzburg-Landau equations. Z. Angew. Math. Mech. 81 (2001), 523–539. [Google Scholar]
  29. T. Tzaneteas, I. M. Sigal. Abrikosov lattice solutions of the Ginzburg-Landau equations. Contemporary Mathematics 535, 195–213, 2011. [CrossRef] [Google Scholar]

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