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Integrable two-component systems of difference equations

2020; Royal Society; Volume: 476; Issue: 2234 Linguagem: Inglês

10.1098/rspa.2019.0668

1471-2946

Pavlos Kassotakis, Maciej Nieszporski, V. Papageorgiou, Anastasios Tongas,

Advanced Topics in Algebra

We present two lists of two-component systems of integrable difference equations defined on the edges of the Z 2 graph. The integrability of these systems is manifested by their Lax formulation which is a consequence of the multi-dimensional compatibility of these systems. Imposing constraints consistent with the systems of difference equations, we recover known integrable quad-equations including the discrete version of the Krichever–Novikov equation. The systems of difference equations give us in turn quadrirational Yang–Baxter maps.