Geodesic
An~algebraic method for classifying S-integrable discrete models
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 407-419

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We discuss a method for classifying integrable equations on quad-graphs based on algebraic ideas. We assign a Lie ring to the equation and study the function describing the dimensions of linear spaces spanned by multiple commutators of the ring generators. This function grows exponentially in the general case. Examples show that it grows more slowly for integrable equations. We propose a classification scheme based on this observation.
Keywords: quad-graph equation, characteristic vector field, Lie ring, integrability condition, discrete KdV equation.
Mots-clés : classification 
@article{TMF_2011_167_3_a6,
     author = {I. T. Habibullin and E. V. Gudkova},
     title = {An~algebraic method for classifying {S-integrable} discrete models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {407--419},
     publisher = {mathdoc},
     volume = {167},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a6/}
}
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I. T. Habibullin; E. V. Gudkova. An~algebraic method for classifying S-integrable discrete models. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 3, pp. 407-419. http://geodesic.mathdoc.fr/item/TMF_2011_167_3_a6/