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2001 Integrable systems in the infinite genus limit
Fritz Gesztesy
Differential Integral Equations 14(6): 671-700 (2001). DOI: 10.57262/die/1356123242


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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Fritz Gesztesy. "Integrable systems in the infinite genus limit." Differential Integral Equations 14 (6) 671 - 700, 2001.


Published: 2001
First available in Project Euclid: 21 December 2012

zbMATH: 1161.35486
MathSciNet: MR1826956
Digital Object Identifier: 10.57262/die/1356123242

Primary: 37K20
Secondary: 14H70 , 35Q53 , 35Q55 , 35Q58 , 37K10

Rights: Copyright © 2001 Khayyam Publishing, Inc.

Vol.14 • No. 6 • 2001
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