Classification of 3D consistent quad-equations

Details Classification of 3D consistent quad-equations Classification of 3D consistent quad-equations

2010-09-21

arxiv.org/abs/1009.4007v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

31 pages

Scientific paper

We consider 3D consistent systems of six independent quad-equations assigned to the faces of a cube. The well-known classification of 3D consistent quad-equations, the so-called ABS-list, is included in this situation. The extension of these equations to the whole lattice Z^3 is possible by reflecting the cubes. For every quad-equation we will give at least one system included leading to a B\"acklund transformation and a zero-curvature representation which means that they are integrable.

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