Integrable Systems in the Infinite Genus Limit

Details Integrable Systems in the Infinite Genus Limit Integrable Systems in the Infinite Genus Limit

1999-07-07

arxiv.org/abs/solv-int/9907009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX, 24 pages

Scientific paper

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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