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On Abrikosov Lattice Solutions of the Ginzburg-Landau Equation

Published online by Cambridge University Press:  17 September 2013

T. Tzaneteas  and
I.M. Sigal
T. Tzaneteas*
Affiliation:
Department of Mathematics, Aarhus University, Aarhus, Denmark
I.M. Sigal*
Affiliation:
Dept. of Mathematics, Univ. of Toronto, Toronto, Canada, M5S 2E4
*
⋆ Corresponding author. E-mail: ttzaneteas@imf.au.dk
⋆⋆ Corresponding author. E-mail: im.sigal@utoronto.ca
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Abstract

Building on earlier work, we have given in [29] a proof of existence of Abrikosov vortex lattices in the Ginzburg-Landau model of superconductivity and shown that the triangular lattice gives the lowest energy per lattice cell. After [29] was published, we realized that it proves a stronger result than was stated there. This result is recorded in the present paper. The proofs remain the same as in [29], apart from some streamlining.

Keywords

magnetic vorticessuperconductivityGinzburg-Landau equationsAbrikosov vortex latticesbifurcation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 5: Bifurcations , 2013 , pp. 190 - 205
Copyright
© EDP Sciences, 2013

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