  We study soliton solutions in 1+1 dimensional gauged sigma models, obtained
by dimensional reduction from its 2+1 dimensional counterparts. We show that
the Bogomol'nyi bound of these models can be expressed in terms of two
conserved charges in a similar way to that of the BPS dyons in 3+1 dimensions.
Purely magnetic vortices of the 2+1 dimensional completely gauged sigma model
appear as charged solitons in the corresponding 1+1 dimensional theory. The
scale invariance of these solitons is also broken because of the dimensional
reduction. We obtain exact static soliton solutions of these models saturating
the Bogomol'nyi bound.
