Abstract
The structure of periodic solutions to the Ginzburg–Landau
equations in R2 is studied in the
critical case, when the equations may be reduced to the first-order Bogomolnyi equations. We
prove the existence of periodic solutions when the area of the fundamental cell is greater than
4πM, M being the overall order of the vortices within
the fundamental cell (the topological
invariant). For smaller fundamental cell areas, it is shown that no periodic solution exists.
It is then proved that as the boundaries of the fundamental cell go to infinity, the periodic
solutions tend to Taubes' arbitrary N-vortex solution.
Publisher
Cambridge University Press (CUP)
Cited by
1 articles.
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