Searching for CAC-maps

By Jarmo Hietarinta. 2005

85 citations recorded by the source corpus.

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 lattice equations assuming also the same symmetry properties, but not the tetrahedron property.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/85e89c60d6020e6f14de81f3da47bf86c6699799

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. James Atkinson
2. F. Nijhoff

In Statistical and Nonlinear Physics

1. James Atkinson
2. F. Nijhoff
3. Jarmo Hietarinta
4. Sergei Silvestrov
5. Daniel S. D. Larsson

Citations in the corpus

• Symmetries of Integrable Difference Equations on the Quad‐Graph (2007, unknown): “We use the same titles for equations as were used in [1], except that Q4 is given in the equivalent form due to Hietarinta [12].”
• Soliton Solutions for ABS Lattice Equations (2009, background): “1d), which in this form was first presented in [15].”
• Soliton solutions for ABS lattice equations: I. Cauchy matrix approach (2009, background): “1d), which in this form was first presented in [15].”