  The existence of singularities of the solution for a class of Lax equations
is investigated using a development of the fac- torization method first
proposed by Semenov-Tian-Shansky and Reymann [11], [9]. It is shown that the
existence of a singularity at a point t = ti is directly related to the
property that the ker- nel of a certain Toeplitz operator (whose symbol depends
on t) be non-trivial. The investigation of this question involves the factor-
ization on a Riemann surface of a scalar function closely related to the
above-mentioned operator. An example is presented and the set of singularities
is shown to coincide with the set obtained by classical methods. This
comparison involves relating the two Riemann surfaces associated to the system
by these methods.
