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Teoreticheskaya i Matematicheskaya Fizika, 2011, Volume 167, Number 3, Pages 407–419
DOI: https://doi.org/10.4213/tmf6650 (Mi tmf6650) 		 
This article is cited in 6 scientific papers (total in 6 papers)

An algebraic method for classifying S-integrable discrete models

I. T. Habibullina, E. V. Gudkovab

a Ufa Institute of Mathematics, RAS, Ufa, Russia
b Department of Applied Mathematics and Mechanics, Ufa State Petroleum Technical University, Ufa, Russia
Full-text PDF (444 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf6650
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
English version:
Theoretical and Mathematical Physics, 2011, Volume 167, Issue 3, Pages 751–761
DOI: https://doi.org/10.1007/s11232-011-0059-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: I. T. Habibullin, E. V. Gudkova, “An algebraic method for classifying S-integrable discrete models”, TMF, 167:3 (2011), 407–419; Theoret. and Math. Phys., 167:3 (2011), 751–761
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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