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Kassotakis, Pavlos; Nieszporski, Maciej; Papageorgiou, Vassilios; Tongas, Anastasios

Integrable two-component systems of difference equations. (English) Zbl 1439.39005

Proc. R. Soc. Lond., A, Math. Phys. Eng. Sci. 476, No. 2234, Article ID 20190668, 22 p. (2020).
Summary: We present two lists of two-component systems of integrable difference equations defined on the edges of the \(\mathbb{Z}^2\) 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.

Cited in 8 Documents

MSC:

39A14 Partial difference equations

Keywords:

integrable difference equations; Lax pairs; Yang-Baxter maps.
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Full Text: DOI arXiv

References:

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