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

Abstract

We explain how spectrally stable vortices of the Nonlinear Schrödinger 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.

Revised version

References in corpus (10)

• Kink dynamics in the ${\varphi }^4$ model: asymptotic stability for odd perturbations in the energy space
• When Does Linear Stability Not Exclude Nonlinear Instability ?
• Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons
• On instability of excited states of the nonlinear Schrödinger equation
• Freezing of energy of a soliton in an external potential
• Dynamics of Nonlinear Schrodinger / Gross-Pitaevskii Equations; Mass Transfer in Systems with Solitons and Degenerate Neutral Modes
• Equipartition of Mass in Nonlinear Schrödinger / Gross-Pitaevskii Equations
• Existence and asymptotic stability of quasi-periodic solution of discrete NLS with potential in $\mathbb{Z}$
• Asymptotic stability for standing waves of a NLS equation with concentrated nonlinearity in dimension three. II
• Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices

Cited by in corpus (5)

• A survey on asymptotic stability of ground states of nonlinear Schrodinger equations II
• Existence and Stability Properties of Radial Bound States for Schrödinger-Poisson with an External Coulomb Potential in Three Space Dimensions
• Stabilization of small solutions of discrete NLS with potential having two eigenvalues
• Long time oscillation of solutions of nonlinear Schrödinger equations near minimal mass ground state
• On nonlinear profile decompositions and scattering for a NLS-ODE model