Time dependence of the Skyrme soliton

Small oscillations of the static Skyrme soliton are considered. It is found that the Skyrme soliton is stable against small oscillations and there is no bound state. The meson-soliton scattering phase shifts are calculated. A resonance is found at \ensuremath{\sim}250-300 MeV above the nucleon, which is only halfway from the Roper resonance ${N}^{*}(1440)$. Small oscillations are also considered for spinning Skyrme solitons. The results are similar. Some implications and difficulties associated with spinning solitons are discussed.