- 03-246 Fritz Gesztesy, Karl Unterkofler, and Rudi Weikard
- On a Theorem of Halphen and its Application to Integrable Systems
May 29, 03
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Abstract. We extend Halphen's theorem which characterizes the solutions
of certain nth-order differential equations with rational
coefficients and meromorphic fundamental systems to a
first-order n x n system of differential equations.
As an application of this circle of ideas we consider stationary
rational algebro-geometric solutions of the KdV hierarchy and
illustrate some of the connections with completely integrable
models of the Calogero-Moser-type. 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
Airault-McKean-Moser locus of their poles.