## On orbital instability of spectrally stable vortices of the NLS in the plane.(English)Zbl 1360.35240

Summary: 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.

### MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35B35 Stability in context of PDEs

### Keywords:

stability; Krein signature
Full Text:

### References:

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