An algebraic method of classification of S-integrable discrete models

Details An algebraic method of classification of S-integrable discrete models An algebraic method of classification of S-integrable discrete models

2010-06-17

arxiv.org/abs/1006.3423v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages, workshop "Nonlinear Physics. Theory and Experiment VI", submitted to TMF

Scientific paper

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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