Quadrirational Yang-Baxter maps and the elliptic Cremona system

2018/04/05 by James Atkinson, Atkinson, James, Yasuhiko Yamada +1
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1804.01794

openalex publication_date 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper connects the quadrirational Yang-Baxter maps, which are two-dimensional integrable discrete systems of KdV type, and the elliptic Cremona system, which is a higher analogue of discrete Painlevé equations associated with E₈ symmetry. This is a natural connection between integrable systems in different dimensions that is outside of the usual paradigm of reductions. Our approach is based on formulation of both systems in terms of birational Coxeter groups.

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