  A gauged (2+1)-dimensional version of the Skyrme model is investigated. The
gauge group is $U(1)$ and the dynamics of the associated gauge potential is
governed by a Maxwell term. In this model there are topologically stable
soliton solutions carrying magnetic flux which is not topologically quantized.
The properties of rotationally symmetric solitons of degree one and two are
discussed in detail. It is shown that the electric field for such solutions is
necessarily zero. The solitons' shape, mass and magnetic flux depend on the
$U(1)$ coupling constant, and this dependence is studied numerically from very
weak to very strong coupling.
