An explicit characterization of Calogero–Moser systems

Gesztesy, Fritz; Unterkofler, Karl; Weikard, Rudi

doi:10.1090/S0002-9947-05-03886-9

An explicit characterization of Calogero–Moser systems
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by Fritz Gesztesy, Karl Unterkofler and Rudi Weikard PDF

Trans. Amer. Math. Soc. 358 (2006), 603-656

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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