On a Theorem of Halphen and its Application to Integrable Systems

Academic Article

Abstract

  • 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×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. © 2000 Academic Press.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Gesztesy F; Unterkofler K; Weikard R
  • Start Page

  • 504
  • End Page

  • 526
  • Volume

  • 251
  • Issue

  • 2