Exact N-vortex solutions to the Ginzburg-Landau equations for kappa=1/sqrt(2)

TL;DR

This paper derives exact N-vortex solutions for the two-dimensional Ginzburg-Landau equations at the critical kappa value, focusing on large flux vortices and their core shapes using complex analysis methods.

Contribution

It provides the first exact solutions for large N vortices at the critical kappa, advancing understanding of vortex core structures in this regime.

Findings

Exact solutions for large N vortices at kappa=1/√2

Vortex core shape determined analytically

Reduction of the problem to a boundary value problem

Abstract

The N-vortex solutions to the two-dimensional Ginzburg - Landau equations for the kappa=1/\sqrt(2) parameter are built. The exact solutions are derived for the vortices with large numbers of the magnetic flux quanta. The size of vortex core is supposed to be much greater than the magnetic field penetration depth. In this limiting case the problem is reduced to the determination of vortex core shape. The corresponding nonlinear boundary problem is solved by means of the methods of the theory of analytic functions.