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TMF, 2018, Volume 197, Number 3, Pages 444–463 (Mi tmf9569)  

This article is cited in 1 scientific paper (total in 1 paper)

Higher Hirota difference equations and their reductions

A. K. Pogrebkov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

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).


DOI: https://doi.org/10.4213/tmf9569

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English version:
Theoretical and Mathematical Physics, 2018, 197:3, 1779–1796

Bibliographic databases:

Received: 22.02.2018

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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  • http://mi.mathnet.ru/eng/tmf/v197/i3/p444

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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. 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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