dorsal/arxiv
View SchemaIntegrable Systems in the Infinite Genus Limit
| Authors | Fritz Gesztesy |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9907009 |
| URL | https://arxiv.org/abs/solv-int/9907009 |
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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"abstract": "We provide an elementary approach to integrable systems associated with\nhyperelliptic curves of infinite genus. In particular, we explore the extent to\nwhich the classical Burchnall-Chaundy theory generalizes in the infinite genus\nlimit, and systematically study the effect of Darboux transformations for the\nKdV hierarchy on such infinite genus curves. Our approach applies to\ncomplex-valued periodic solutions of the KdV hierarchy and naturally identifies\nthe Riemann surface familiar from standard Floquet theoretic considerations\nwith a limit of Burchnall-Chaundy curves.",
"arxiv_id": "solv-int/9907009",
"authors": [
"Fritz Gesztesy"
],
"categories": [
"solv-int",
"nlin.SI"
],
"title": "Integrable Systems in the Infinite Genus Limit",
"url": "https://arxiv.org/abs/solv-int/9907009"
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