Integrable multi-component difference systems of equations

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.

arXiv comment23 pages

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Cited by in corpus (1)

• Multi-Component Extension of CAC Systems