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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 3, Pages 433–446
DOI: https://doi.org/10.4213/tmf9204 (Mi tmf9204) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions

A. K. Pogrebkov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (412 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf9204
Abstract: We show that the non-Abelian Hirota difference equation is directly related to a commutator identity on an associative algebra. Evolutions generated by similarity transformations of elements of this algebra lead to a linear difference equation. We develop a special dressing procedure that results in an integrable non-Abelian Hirota difference equation and propose two regular reduction procedures that lead to a set of known equations, Abelian or non-Abelian, and also to some new integrable equations.
Keywords: integrable equation, commutator identity, reduction.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This research was performed at the Steklov Mathematical Institute of Russian Academy of Sciences and was funded by a grant from the Russian Science Foundation (Project No. 14-50-00005).
Received: 11.04.2016
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 3, Pages 823–834
DOI: https://doi.org/10.1134/S0040577916060039
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. K. Pogrebkov, “Commutator identities on associative algebras, the non-Abelian Hirota difference equation and its reductions”, TMF, 187:3 (2016), 433–446; Theoret. and Math. Phys., 187:3 (2016), 823–834
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
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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