Integrable systems whose spectral curve is the graph of a function

Kanehisa Takasaki

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arXiv · nlin/0211021

Integrable systems whose spectral curve is the graph of a function

Kanehisa Takasaki

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Abstract

For some integrable systems, such as the open Toda molecule, the spectral curve of the Lax representation becomes the graph $C = \{(λ,z) \mid z = A(λ)\}$ of a function $A(λ)$. 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 $A(λ)$ lives on a cylinder, a torus or a Riemann surface of higher genus.

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Kanehisa Takasaki. 2004-04-23. Integrable systems whose spectral curve is the graph of a function. https://arxiv.org/abs/nlin/0211021

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