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On a Theorem of Halphen and its Application to Integrable Systems

✍ Scribed by F Gesztesy; K Unterkofler; R Weikard

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
166 KB
Volume
251
Category
Article
ISSN
0022-247X

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✦ Synopsis

We extend Halphen's theorem which characterizes solutions of certain nth-order differential equations with rational coefficients and meromorphic fundamental systems to a first-order n Γ— 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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