Aftalion, Amandine and Chapman, S. J. (2000) Asymptotic analysis of a secondary bifurcation of the onedimensional GinzburgLandau equations of superconductivity. SIAM Journal on Applied Mathematics, 60 (4). pp. 11571176. ISSN 1095712X

PDF
201kB 
Official URL: http://www.siam.org/journals/siap/604/34479.html
Abstract
The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the onedimensional GinzburgLandau 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 , the GinzburgLandau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of for which it is close to the primary bifurcation from the normal state. These values of form a curve in the 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. 214232].
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:  29 May 2015 18:25 
Repository Staff Only: item control page