Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2002-11-15
Nonlinear Sciences
Exactly Solvable and Integrable Systems
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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