  We consider a general ansatz for solving the 2-dimensional Hitchin's
equations, which arise as dimensional reduction of the 4-dimensional self-dual
Yang-Mills equations, with remarkable integrability properties. We focus on the
case when the gauge group G is given by a real form of SL(2,C). For G=SO(2,1),
the resulting field equations are shown to reduce to either the Liouville,
elliptic sinh-Gordon or elliptic sine-Gordon equations. As opposed to the
compact case, given by G=SU(2), the field equations associated with the
noncompact group SO(2,1) are shown to have smooth real solutions with
nonsingular action densities, which are furthermore localized in some sense. We
conclude by discussing some particular solutions, defined on R^2, S^2 and T^2,
that come out of this ansatz.
