Integrable Systems in the Infinite Genus Limit

Fritz Gesztesy

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Integrable Systems in the Infinite Genus Limit

Fritz Gesztesy

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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 Burchnall-Chaundy 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 complex-valued periodic solutions of the KdV hierarchy and naturally identifies the Riemann surface familiar from standard Floquet theoretic considerations with a limit of Burchnall-Chaundy curves.

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BibTeX RIS

Fritz Gesztesy. 1999-07-07. Integrable Systems in the Infinite Genus Limit. https://arxiv.org/abs/solv-int/9907009

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