Tetrahedron maps and symmetries of three dimensional integrable discrete equations

Pavlos Kassotakis; Maciej Nieszporski; Vassilios Papageorgiou; Anastasios Tongas

doi:10.1063/1.5124874

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arXiv · 1908.03019

Tetrahedron maps and symmetries of three dimensional integrable discrete equations

Pavlos Kassotakis·Maciej Nieszporski·Vassilios Papageorgiou·Anastasios Tongas

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Abstract

A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on $\mathbb{Z}^3$ is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter maps, based on the invariants of symmetry groups of the lattice equations. The method is demonstrated by a case-by-case analysis of the octahedron type lattice equations classified recently, leading to some new examples of tetrahedron maps and integrable coupled lattice equations.

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Pavlos Kassotakis, Maciej Nieszporski, Vassilios Papageorgiou, Anastasios Tongas. 2019-08-08. Tetrahedron maps and symmetries of three dimensional integrable discrete equations. https://doi.org/10.1063/1.5124874

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