On orbital instability of spectrally stable vortices of the NLS in the plane

TL;DR

This paper investigates how spectrally stable vortices in the nonlinear Schrödinger equation can still be orbitally unstable due to nonlinear interactions, highlighting the role of the nonlinear Fermi golden rule.

Contribution

It demonstrates the mechanism by which spectral stability does not guarantee orbital stability for vortices in the NLS, emphasizing the nonlinear Fermi golden rule's role.

Findings

Spectrally stable vortices can be orbitally unstable.

Nonlinear interactions between modes cause instability.

The nonlinear Fermi golden rule explains this instability.

Abstract

We explain how spectrally stable vortices of the Nonlinear Schr\"odinger Equation in the plane can be orbitally unstable. This relates to the nonlinear Fermi golden rule, a mechanism which exploits the nonlinear interaction between discrete and continuous modes of the NLS.