Radial vibrations of BPS skyrmions

We study radial vibrations of spherically symmetric Skyrmions in the Bogomol'nyi-Prasad-Sommerfield Skyrme model. Concretely, we numerically solve the linearized field equations for small fluctuations in a Skyrmion background, both for linearly stable oscillations and for (unstable) resonances. This is complemented by numerical solutions of the full nonlinear system, which confirm all the results of the linear analysis. In all cases, the resulting fundamental excitation provides a rather accurate value for the Roper resonance, supporting the hypothesis that the Bogomol'nyi-Prasad-Sommerfield Skyrme model already gives a reasonable approximate description of this resonance. Furthermore, for many potentials additional higher resonances appear, again in agreement with known experimental results.