An algebraic method of classification of S-integrable discrete models
Exactly Solvable and Integrable Systems
2015-05-19 v2
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.
Cite
@article{arxiv.1006.3423,
title = {An algebraic method of classification of S-integrable discrete models},
author = {Ismagil T. Habibullin and Elena V. Gudkova},
journal= {arXiv preprint arXiv:1006.3423},
year = {2015}
}
Comments
11 pages, workshop "Nonlinear Physics. Theory and Experiment VI", submitted to TMF