Integrable systems whose spectral curve is the graph of a function
Abstract
For some integrable systems, such as the open Toda molecule, the spectral curve of the Lax representation becomes the graph $C = \{(\lambda,z) \mid z = A(\lambda)\}$ of a function $A(\lambda)$. Those integrable systems provide an interesting ``toy model'' of separation of variables. Examples of this type of integrable systems are presented along with generalizations for which $A(\lambda)$ lives on a cylinder, a torus or a Riemann surface of higher genus.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2002
- DOI:
- 10.48550/arXiv.nlin/0211021
- arXiv:
- arXiv:nlin/0211021
- Bibcode:
- 2002nlin.....11021T
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- High Energy Physics - Theory;
- Mathematical Physics;
- Mathematics - Mathematical Physics
- E-Print:
- latex2e, 15 pages, no figure