An explicit characterization of Calogero-Moser systems |
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| Authors: | Fritz Gesztesy Karl Unterkofler Rudi Weikard |
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| Institution: | Department of Mathematics, University of Missouri, Columbia, Missouri 65211 ; Department of Computer Science, Applied Mathematics Group, FH-Vorarlberg, A--6850 Dornbirn, Austria ; Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294--1170 |
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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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| Keywords: | Rational solution simply periodic solution elliptic KdV solution Calogero--Moser systems Halphen theorem Floquet theorem Picard theorem KdV hierarchy |
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