This article is cited in 6 papers

An algebraic method for classifying S-integrable discrete models

I. T. Habibullin^a, E. V. Gudkova<sup>b

a</sup> Ufa Institute of Mathematics, RAS, Ufa, Russia
^b Department of Applied Mathematics and Mechanics, Ufa State Petroleum Technical University, Ufa, Russia

Abstract: 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, classification, characteristic vector field, Lie ring, integrability condition, discrete KdV equation.

Received: 23.06.2011

DOI: 10.4213/tmf6650

 English version: Theoretical and Mathematical Physics, 2011, 167:3, 751–761

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