Yang-Baxter maps associated to elliptic curves

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.

16 pages, 4 figures

References in corpus (5)

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• Yang-Baxter maps and symmetries of integrable equations on quad-graphs
• On Discrete 3-Dimensional Equations Associated with the Local Yang-Baxter Relation
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Cited by in corpus (10)

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• On the $3D$ consistency of a Grassmann extended lattice Boussinesq system
• On the Lagrangian formulation of multidimensionally consistent systems
• Poisson structures for lifts and periodic reductions of integrable lattice equations
• Relativistic Collisions as Yang-Baxter maps
• Birational solutions to the set-theoretical 4-simplex equation
• Integrable multi-component difference systems of equations
• ${\mathbb{Z}}_N$ graded discrete Lax pairs and Yang-Baxter maps