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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 197, Number 3, Pages 444–463
DOI: https://doi.org/10.4213/tmf9569
(Mi tmf9569)
 

This article is cited in 3 scientific papers (total in 3 papers)

Higher Hirota difference equations and their reductions

A. K. Pogrebkov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (505 kB) Citations (3)
References:
Abstract: We previously proposed an approach for constructing integrable equations based on the dynamics in associative algebras given by commutator relations. In the framework of this approach, evolution equations determined by commutators of (or similarity transformations with) functions of the same operator are compatible by construction. Linear equations consequently arise, giving a base for constructing nonlinear integrable equations together with the corresponding Lax pairs using a special dressing procedure. We propose an extension of this approach based on introducing higher analogues of the famous Hirota difference equation. We also consider some $(1+1)$-dimensional discrete integrable equations that arise as reductions of either the Hirota difference equation itself or a higher equation in its hierarchy.
Keywords: integrability, commutator identity, Hirota difference equation, higher integrable equation, reduction.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This research is supported by a grant from the Russian Science Foundation (Project No. 14-50-00005).
Received: 22.02.2018
English version:
Theoretical and Mathematical Physics, 2018, Volume 197, Issue 3, Pages 1779–1796
DOI: https://doi.org/10.1134/S0040577918120085
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. K. Pogrebkov, “Higher Hirota difference equations and their reductions”, TMF, 197:3 (2018), 444–463; Theoret. and Math. Phys., 197:3 (2018), 1779–1796
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9569
  • https://doi.org/10.4213/tmf9569
  • https://www.mathnet.ru/eng/tmf/v197/i3/p444
  • This publication is cited in the following 3 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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    Abstract page:314
    Full-text PDF :67
    References:40
    First page:8
     
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