Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube

Abstract

There is a recently discovered formulation of the multidimensional consistency integrability condition for lattice equations, called consistency-around-a-face-centered-cube(CAFCC), which is applicable to equations defined on a vertex and its four nearest neighbours on the square lattice. This paper introduces a method of deriving Lax matrices for the equations which satisfy CAFCC. This method gives novel Lax matrices for such equations, which include previously known equations of discrete Toda-, or Laplace-type, as well as newer equations which have only appeared in the context of CAFCC.

30 pages, 10 figures, v2: minor edits and typos

References in corpus (4)

• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Boussinesq-like multi-component lattice equations and multi-dimensional consistency
• Multi-Component Extension of CAC Systems
• Interaction-round-a-face and consistency-around-a-face-centered-cube

Cited by in corpus (3)

• Algebraic entropy for face-centered quad equations
• Discrete integrable equations on face-centered cubics: consistency and Lax pairs of corner equations
• Quasi-classical expansion of a hyperbolic solution to the star-star relation and multicomponent 5-point difference equations