An explicit Characterization of Calogero-Moser Systems
F. Gesztesy, K. Unterkofler, and R. Weikard (2006): 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 Calogero-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. www.ams.org
