 99261 Fritz Gesztesy
 Integrable Systems in the Infinite Genus Limit
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Jul 7, 99

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Abstract. We provide an elementary approach to integrable systems associated
with hyperelliptic curves of infinite genus. In particular, we
explore the extent to which the classical BurchnallChaundy theory
generalizes in the infinite genus limit, and systematically study
the effect of Darboux transformations for the KdV hierarchy on such
infinite genus curves. Our approach applies to complexvalued
periodic solutions of the KdV hierarchy and naturally identifies
the Riemann surface familiar from standard Floquet theoretic
considerations with a limit of BurchnallChaundy curves.
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