An algebraic method of classification of S-integrable discrete models

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.

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

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Cited by in corpus (3)

• Generalized symmetry integrability test for discrete equations on the square lattice
• Characteristic Lie rings, finitely-generated modules and integrability conditions for 2+1 dimensional lattices
• Classification of integrable discrete Klein-Gordon models