On asymptotic stability of the Skyrmion

TL;DR

This paper analyzes the long-term behavior of spherically symmetric solutions in the Skyrme model, revealing a universal relaxation pattern consisting of damped oscillations and power-law decay.

Contribution

It demonstrates that the relaxation to the Skyrmion involves both linear quasinormal ringing and nonlinear tail decay, providing a detailed understanding of the asymptotic dynamics.

Findings

Quasinormal ringing dominates intermediate times

Power law tail appears at late times

Tail decay is a nonlinear effect

Abstract

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.