Yang-Baxter maps associated to elliptic curves
Vassilios G. Papageorgiou, Anastasios G. Tongas
TL;DR
This paper introduces Yang-Baxter maps linked to elliptic curves, connecting them to discrete integrable equations and demonstrating a lifting process from scalar to two-field equations.
Contribution
It presents new Yang-Baxter maps associated with elliptic curves and extends scalar integrable equations to two-field systems.
Findings
Yang-Baxter maps related to elliptic curves are constructed.
Connections to discrete Krichever-Novikov and Landau-Lifshitz equations are established.
A method for lifting scalar equations to two-field equations is demonstrated.
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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Advanced Topics in Algebra