Atlantis Press Paper Details: Searching for CAC-maps

For two-dimensional lattice equations the standard definition of integrability is that it should be possible to extend the map consistently to three dimensions, i.e., that it is "consistent around a cube" (CAC). Recently Adler, Bobenko and Suris conducted a search based on this principle, together with the additional assumptions of symmetry and "the tetrahedron property". We present here results of a search for CAC latice equations assuming also the same symmetry properties, but not the tetrahedron property.


title:		Searching for CAC-maps
publication:		JNMP
volume-issue:		12 - Supplement 2
pages:		223 - 230
ISSN:		1402-9251
DOI:		doi:10.2991/jnmp.2005.12.s2.16 (how to use a DOI)
author(s):		Jarmo HIETARINTA
publication date:		December 2005
abstract:		For two-dimensional lattice equations the standard definition of integrability is that it should be possible to extend the map consistently to three dimensions, i.e., that it is "consistent around a cube" (CAC). Recently Adler, Bobenko and Suris conducted a search based on this principle, together with the additional assumptions of symmetry and "the tetrahedron property". We present here results of a search for CAC latice equations assuming also the same symmetry properties, but not the tetrahedron property.
copyright:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		12s2_16n.pdf (108 K)