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Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity

Aftalion, Amandine and Chapman, S. J. (2000) Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity. SIAM Journal on Applied Mathematics, 60 (4). pp. 1157-1176. ISSN 1095-712X

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Abstract

The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232].

Item Type:Article
Uncontrolled Keywords:superconducting; bifurcation; symmetric; asymmetric
Subjects:O - Z > Optics, electromagnetic theory
O - Z > Ordinary differential equations
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:605
Deposited By:Jon Chapman
Deposited On:24 May 2007
Last Modified:20 Jul 2009 14:22

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