Integrable systems whose spectral curve is the graph of a function

Nonlinear Sciences – Exactly Solvable and Integrable Systems

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latex2e, 15 pages, no figure; (v2) typos in eq. (25) etc. are corrected; (v3) a few typos are corrected. This article will be

Scientific paper

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.

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