English

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

Mathematical Physics 2021-09-17 v2 math.MP Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.2007.01196,
  title  = {Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube},
  author = {Andrew P. Kels},
  journal= {arXiv preprint arXiv:2007.01196},
  year   = {2021}
}

Comments

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

R2 v1 2026-06-23T16:48:20.472Z