Stability of symmetric vortices for two-component Ginzburg-Landau systems

TL;DR

This paper investigates the stability of symmetric vortex solutions in two-component Ginzburg-Landau systems, revealing how stability depends on system parameters and interaction signs.

Contribution

It provides a detailed spectral analysis of the second variation of energy for symmetric vortices in two-component Ginzburg-Landau equations, highlighting parameter-dependent stability.

Findings

Stability depends on the Ginzburg-Landau parameter.

Sign of the interaction term influences stability.

Spectral analysis characterizes stability conditions.

Abstract

We study Ginzburg-Landau equations for a complex vector order parameter. We consider the Dirichlet problem in the disk in the plane with a symmetric, degree-one boundary condition, and study its stability, in the sense of the spectrum of the second variation of the energy. We find that the stability of the degree-one equivariant solution depends on both the Ginzburg-Landau parameter as well as the sign of the interaction term in the energy.