# Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

## TL;DR

This paper proves the existence of Abrikosov vortex lattice solutions within the Ginzburg-Landau model of superconductivity, extending previous foundational work in the field.

## Contribution

It provides a rigorous proof of Abrikosov lattice solutions, advancing mathematical understanding of vortex arrangements in superconductors.

## Key findings

- Existence of Abrikosov vortex lattices established.
- Mathematical framework for vortex lattice solutions developed.
- Builds on and extends prior foundational work.

## Abstract

Building on the earlier work of Odeh, Barany, Golubitsky, Turski and Lasher we give a proof of existence of Abrikosov vortex lattices in the Ginzburg-Landau model of superconductivity.