  We consider the Riemann-Hilbert factorization approach to solving the field
equations of dimensionally reduced gravity theories. First we prove that
functions belonging to a certain class possess a canonical factorization due to
properties of the underlying spectral curve. Then we use this result, together
with appropriate matricial decompositions, to study the canonical factorization
of non-meromorphic monodromy matrices that describe deformations of seed
monodromy matrices associated with known solutions. This results in new
solutions, with unusual features, to the field equations.
