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arXiv · 1009.4007

Classification of 3D consistent quad-equations

Raphael Boll
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Abstract

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 Bäcklund transformation and a zero-curvature representation which means that they are integrable.

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Raphael Boll. 2010-11-03. Classification of 3D consistent quad-equations. https://doi.org/10.1142/s1402925111001647

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