Elliptic solutions to difference non-linear equations and nested Bethe ansatz equations

1998/04/15 by I. M. Krichever, Krichever, I. M.
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #hep-th #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9804016

21 pages, Latex, no figures

arxiv created 1998/04/15 · openalex publication_date 1998/04/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We outline an approach to a theory of various generalizations of the elliptic Calogero-Moser (CM) and Ruijsenaars-Shneider (RS) systems based on a special inverse problem for linear operators with elliptic coefficients. Hamiltonian theory of such systems is developed with the help of the universal symplectic structure proposed by D.H. Phong and the author. Canonically conjugated action-angle variables for spin generalizations of the elliptic CM and RS systems are found.

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