Multisolitons in a gauged Skyrme-Maxwell model

We construct new solutions of a $U(1)$ gauged Skyrme-Maxwell model of topological degrees $Q\le 5$, which represent Skyrmions coupled to magnetic fluxes. It is found that, generically, in the strong coupling limit, coupling to the magnetic field results in transformation of the configuration to the toroidally shaped Skyrmions bounded to the local magnetic flux.