Two new families of integrable multi-component difference systems in bond variables are constructed, with Lax pairs, Yang-Baxter maps, and reductions to the ABS quad-equations.
Yang-Baxter maps associated to elliptic curves
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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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Integrable multi-component difference systems of equations
Two new families of integrable multi-component difference systems in bond variables are constructed, with Lax pairs, Yang-Baxter maps, and reductions to the ABS quad-equations.