Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Asymptotic analysis of the one-dimensional Ginzburg-Landau equations near self-duality


Author: Y. Almog
Journal: Quart. Appl. Math. 57 (1999), 355-367
MSC: Primary 35Q55; Secondary 34B15, 34E20, 82D55
DOI: https://doi.org/10.1090/qam/1686194
MathSciNet review: MR1686194
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Abstract: It is known that when the Ginzburg-Landau parameter $ k = 1/\sqrt 2$ the one-dimensional Ginzburg-Landau equations exhibit self-duality and may be reduced into a pair of first-order ODE. The present asymptotic analysis initially focuses on infinite samples of superconductors for which $ \left\vert {k - 1/\sqrt 2 } \right\vert \ll 1$. It is shown that when the value of the applied magnetic field at infinity lies between $ k$ and $ 1/\sqrt 2 $ a superconducting solution exists. It is later shown, for arbitrary values of $ k$, that no solution, other than the normal state, can exist for applied magnetic field values that lie outside the above interval.


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DOI: https://doi.org/10.1090/qam/1686194
Article copyright: © Copyright 1999 American Mathematical Society


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