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TMF, 2016, Volume 187, Number 3, Pages 433–446 (Mi tmf9204)  

This article is cited in 4 scientific papers (total in 4 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

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).


DOI: https://doi.org/10.4213/tmf9204

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English version:
Theoretical and Mathematical Physics, 2016, 187:3, 823–834

Bibliographic databases:

Received: 11.04.2016

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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  • https://doi.org/10.4213/tmf9204
  • http://mi.mathnet.ru/eng/tmf/v187/i3/p433

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.  mathnet  crossref  mathscinet
    2. V. V. Zharinov, “Lie–Poisson structures over differential algebras”, Theoret. and Math. Phys., 192:3 (2017), 1337–1349  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. A. K. Pogrebkov, “Higher Hirota difference equations and their reductions”, Theoret. and Math. Phys., 197:3 (2018), 1779–1796  mathnet  crossref  crossref  adsnasa  isi  elib
    4. Pogrebkov A., “Hirota Difference Equation and Darboux System: Mutual Symmetry”, Symmetry-Basel, 11:3 (2019), 436  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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