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arXiv 2007.011962020-07math-phmath.MPnlin.SI

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

Andrew P. Kels

备注：: 30 pages, 10 figures, v2: minor edits and typos
发表信息：: 2021 Nonlinearity 34 7064
DOI：: 10.1088/1361-6544/ac1f76

英文摘要：

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.

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