Integrable Systems with Pairwise Interactions and Functional Equations

1994/11/30 by H. W. Braden, V. M. Buchstaber, Victor Matveevich Buchstaber +2 · 4 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9411240

32 pages latex2e. Some Proofs removed. New Examples

openalex publication_date 1994/11/30 · arxiv created 1996/04/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as well as their relativistic generalisations. The ansatz leads to a system of functional equations. Several new functional equations are described and the general analytic solution to some of these is given. New integrable systems are described.

Cited by

• On a Functional Equation of Ruijsenaars
• Multi-Dimensional Sigma-Functions
• Instantons, Hilbert Schemes and Integrability
• Functional Equations and Poincare Invariant Mechanical Systems

Related

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