An Explicit Characterization of Calogero--Moser Systems

Details An Explicit Characterization of Calogero--Moser Systems An Explicit Characterization of Calogero--Moser Systems

2003-05-29

arxiv.org/abs/nlin/0305057v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 52 pages

Scientific paper

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.

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