Vassilios Papageorgiou

arXiv2019

Tetrahedron maps and symmetries of three dimensional integrable discrete equations

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.

nlin.SI↗

arXiv2019

Integrable multi-component difference systems of equations

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.

nlin.SI↗