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arXiv · 1006.3423

An algebraic method of classification of S-integrable discrete models

Ismagil T. Habibullin·Elena V. Gudkova
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Abstract

A method of classification of integrable equations on quad-graphs is discussed 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. For the generic case this function grows exponentially. Examples show that for integrable equations it grows slower. We propose a classification scheme based on this observation.

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Ismagil T. Habibullin, Elena V. Gudkova. 2010-06-17. An algebraic method of classification of S-integrable discrete models. https://doi.org/10.1007/s11232-011-0059-1

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