Differential and Integral Equations

Classification of symmetric vortices for the Ginzburg-Landau equation

Myrto Sauvageot

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This work proposes a description of the set of symmetric vortices, defined as specific solutions of the Ginzburg-Landau equations for a superconducting cylinder with applied magnetic field. It is conducted through a two parameters shooting procedure which relates the behaviour of a symmetric vortex at the center to its behaviour at the boundary. The main result is that, for a given degree $d$, the set of parameters for which such a "shooting" leads to a "response" -- i.e., admissible values for the radius $\bar r$ of the cylinder and the intensity $h$ of the magnetic field -- is a bounded subset in $\mathbb R^2$. This shows in particular that, for large intensities of the applied magnetic field, normal states do not appear as a limit of superconducting vortices of given degree, and that symmetric vortices are not equilibrium states of the system for too large or too low intensities of the applied magnetic field. Moreover, a simpler proof for the existence of bifurcations (a model for phase transitions) from the normal state to superconducting states, as studied in [11], is provided.

Article information

Source
Differential Integral Equations, Volume 19, Number 7 (2006), 721-760.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050347

Mathematical Reviews number (MathSciNet)
MR2235892

Zentralblatt MATH identifier
1212.35131

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 34B15: Nonlinear boundary value problems 35A15: Variational methods 35J55 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09] 47J30: Variational methods [See also 58Exx] 58E50: Applications 82D55: Superconductors

Citation

Sauvageot, Myrto. Classification of symmetric vortices for the Ginzburg-Landau equation. Differential Integral Equations 19 (2006), no. 7, 721--760. https://projecteuclid.org/euclid.die/1356050347


Export citation