Differential and Integral Equations
- Differential Integral Equations
- Volume 14, Number 6 (2001), 671-700.
Integrable systems in the infinite genus limit
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.
Differential Integral Equations, Volume 14, Number 6 (2001), 671-700.
First available in Project Euclid: 21 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37K20: Relations with algebraic geometry, complex analysis, special functions [See also 14H70]
Secondary: 14H70: Relationships with integrable systems 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35Q58 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
Gesztesy, Fritz. Integrable systems in the infinite genus limit. Differential Integral Equations 14 (2001), no. 6, 671--700. https://projecteuclid.org/euclid.die/1356123242