For non-BPS Abelian-Higgs vortices, the normal modes are classified into Derrick-type, Type A, and Type B multipolar families, with k=1 Type A modes as translational zero modes and k>1 Type A modes as the instability modes for lambda>1.
Bogomolny, Stability of classical solutions , Sov
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Spectral structure of fluctuations around $n$-vortices in the Abelian-Higgs model
For non-BPS Abelian-Higgs vortices, the normal modes are classified into Derrick-type, Type A, and Type B multipolar families, with k=1 Type A modes as translational zero modes and k>1 Type A modes as the instability modes for lambda>1.