03-246 Fritz Gesztesy, Karl Unterkofler, and Rudi Weikard

On a Theorem of Halphen and its Application to Integrable Systems (62K, LaTeX) 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.

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