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An explicit characterization of Calogero-Moser systems


Authors: Fritz Gesztesy, Karl Unterkofler and Rudi Weikard
Journal: Trans. Amer. Math. Soc. 358 (2006), 603-656
MSC (2000): Primary 33E05, 34C25, 34M05; Secondary 35Q58, 37K10
DOI: https://doi.org/10.1090/S0002-9947-05-03886-9
Published electronically: September 23, 2005
MathSciNet review: 2177033
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Abstract: Combining theorems of Halphen, Floquet, and Picard and a Frobenius type analysis, we characterize rational, meromorphic simply periodic, and elliptic KdV potentials. In particular, we explicitly describe the proper extension of the Airault-McKean-Moser locus associated with these three classes of algebro-geometric solutions of the KdV hierarchy with special emphasis on the case of multiple collisions between the poles of solutions. This solves a problem left open since the mid-1970s.


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Additional Information

Fritz Gesztesy
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: fritz@math.missouri.edu

Karl Unterkofler
Affiliation: Department of Computer Science, Applied Mathematics Group, FH-Vorarlberg, A–6850 Dornbirn, Austria
Email: karl.unterkofler@fh-vorarlberg.ac.at

Rudi Weikard
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294–1170
Email: rudi@math.uab.edu

DOI: https://doi.org/10.1090/S0002-9947-05-03886-9
Keywords: Rational solution, simply periodic solution, elliptic KdV solution, Calogero--Moser systems, Halphen theorem, Floquet theorem, Picard theorem, KdV hierarchy
Received by editor(s): February 4, 2004
Published electronically: September 23, 2005
Additional Notes: This work is based upon work supported by the US National Science Foundation under Grant No. DMS-9970299.
Article copyright: © Copyright 2005 by the authors

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