Integrable systems whose spectral curve is the graph of a function

2002/11/15 by Kanehisa Takasaki, Takasaki, Kanehisa
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0211021

latex2e, 15 pages, no figure; (v2) typos in eq. (25) etc. are corrected; (v3) a few typos are corrected. This article will be published in CRM Proceedings and Lecture Notes vol. 37

arxiv created 2004/04/23 · arxiv updated 2009/11/30

Abstract

For some integrable systems, such as the open Toda molecule, the spectral curve of the Lax representation becomes the graph C = \(λ,z) | 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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