Weak Lax pairs for lattice equations

Jarmo Hietarinta (1, 2) , Claude Viallet (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
2 Department of Physics and Astronomy [Turku]

We consider various 2D lattice equations and their integrability, from the point of view of 3D consistency, Lax pairs and B¨acklund transformations. We show that these a concepts, which are associated with integrability, are not strictly equivalent. In the course of our analysis, we introduce a number of black and white lattice models, as well as variants of the functional Yang-Baxter equation.

Mots clés: Discrete integrable systems

Domaines: Systèmes Solubles et Intégrables [nlin.SI]; Physique des Hautes Energies - Théorie [hep-th]

Jarmo Hietarinta, Claude Viallet. Weak Lax pairs for lattice equations. 2011. ⟨hal-00593660⟩