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- Title
Classification of Integrable Discrete Equations of Octahedron Type.
- Authors
Adler, Vsevolod E.; Bobenko, Alexander I.; Suris, Yuri B.
- Abstract
We use the consistency approach to classify discrete integrable three-dimensional equations of the octahedron type. They are naturally treated on the root lattice Q(A3) and are consistent on the multi-dimensional lattice Q(AN). Our list includes the most prominent representatives of this class, the discrete KP equation and its Schwarzian (multi-ratio) version, as well as three further equations. The combinatorics and geometry of the octahedron-type equations are explained. In particular, the consistency on the four-dimensional Delaunay cells has its origin in the classical Desargues theorem of projective geometry. The main technical tool used for the classification is the so-called tripodal form of the octahedron-type equations.
- Subjects
DISCRETE systems; THREE-dimensional imaging; EQUATIONS; GEOMETRY; LATTICE theory
- Publication
IMRN: International Mathematics Research Notices, 2012, Vol 2012, Issue 8, p1822
- ISSN
1073-7928
- Publication type
Article