 03246 Fritz Gesztesy, Karl Unterkofler, and Rudi Weikard
 On a Theorem of Halphen and its Application to Integrable Systems
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May 29, 03

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Abstract. We extend Halphen's theorem which characterizes the solutions
of certain nthorder differential equations with rational
coefficients and meromorphic fundamental systems to a
firstorder n x n system of differential equations.
As an application of this circle of ideas we consider stationary
rational algebrogeometric solutions of the KdV hierarchy and
illustrate some of the connections with completely integrable
models of the CalogeroMosertype. In particular, our treatment recovers
the complete characterization of the isospectral class of such rational
KdV solutions in terms of a precise description of the
AiraultMcKeanMoser locus of their poles.
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