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On asymptotic stability of the Skyrmion

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arxiv math-ph/0701037 v3 pith:HCNP7XBZ submitted 2007-01-11 math-ph gr-qchep-thmath.MP

classification math-phgr-qchep-thmath.MP
keywords asymptoticquasinormalringingskyrmiontailtimesbecomesbehavior
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We study the asymptotic behavior of spherically symmetric solutions in the Skyrme model. We show that the relaxation to the degree-one soliton (called the Skyrmion) has a universal form of a superposition of two effects: exponentially damped oscillations (the quasinormal ringing) and a power law decay (the tail). The quasinormal ringing, which dominates the dynamics for intermediate times, is a linear resonance effect. In contrast, the polynomial tail, which becomes uncovered at late times, is shown to be a \emph{nonlinear} phenomenon.

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    Proca balls in a theory with gauge kinetic coupling support a localized spherically symmetric electromagnetic vibrational mode whose spectrum has a delocalization gap and a revival branch.

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