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arXiv · 1908.02413

Integrable multi-component difference systems of equations

Pavlos Kassotakis·Maciej Nieszporski·Vassilios Papageorgiou·Anastasios Tongas
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Abstract

We present two lists of multi-component systems of integrable difference equations defined on the edges of a $\mathbb{Z}^2$ 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 allow us for a straightforward reformulation as Yang-Baxter maps. Certain two-component systems of equation defined on the vertices of a $\mathbb{Z}^2$ lattice, their non-potential form and integrable equations defined on 5-point stencils, are also obtained.

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Pavlos Kassotakis, Maciej Nieszporski, Vassilios Papageorgiou, Anastasios Tongas. 2019-08-07. Integrable multi-component difference systems of equations. https://arxiv.org/abs/1908.02413

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