Yang-Baxter maps associated to elliptic curves

2009/06/17 by Vassilios G. Papageorgiou, Papageorgiou, Vassilios G., Anastasios G. Tongas +1
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #nlin.SI

paper · pdf · doi:10.48550/arxiv.0906.3258

16 pages, 4 figures

arxiv created 2009/06/17 · arxiv updated 2009/12/01

Abstract

We present Yang-Baxter maps associated to elliptic curves. They are related to discrete versions of the Krichever-Novikov and the Landau-Lifshits equations. A lifting of scalar integrable quad-graph equations to two-field equations is also shown.

Related

• From Yang-Baxter maps to integrable quad maps and recurrences
• ℤ_N graded discrete Lax pairs and Yang-Baxter maps
• Classical Yang-Baxter equation and the A_∞-constraint
• Entwining Yang-Baxter maps and integrable lattices
• Quadrirational Yang-Baxter maps and the elliptic Cremona system