On Abrikosov Lattice Solutions of the Ginzburg-Landau Equation

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 t...

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Bibliographic Details
Published in:Mathematical modelling of natural phenomena 2013, Vol.8 (5), p.190-205
Main Authors: Tzaneteas, T., Sigal, I.M.
Format: Article
Language:English
Subjects:
35B32
35Q56
Abrikosov vortex lattices
bifurcation
Ginzburg-Landau equations
magnetic vortices
superconductivity
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Summary: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.
ISSN:0973-5348
1760-6101
DOI:10.1051/mmnp/20138512