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Symmetry, Integrability and Geometry: Methods and Applications, 2017, Volume 13, 053, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2017.053 (Mi sigma1253) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Symmetries of the Hirota Difference Equation

Andrei K. Pogrebkovab

a Steklov Mathematical Institute of Russian Academy of Science, Moscow, Russia
b National Research University Higher School of Economics, Moscow, Russia
Full-text PDF (378 kB) Citations (5)
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DOI: https://doi.org/10.3842/SIGMA.2017.053
Abstract: Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented. Commutativity of these symmetries enables interpretation of their parameters as “times” of the nonlinear integrable partial differential-difference and differential equations. Examples of equations resulting in such procedure and their Lax pairs are given. Besides these, ordinary, symmetries the additional ones are introduced and their action on the Scattering data is presented.
Keywords: Hirota difference equation; symmetries; integrable differential-difference and differential equations; additional symmetries.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation
This work has been funded by the Russian Academic Excellence Project ‘5-100’.
Received: March 31, 2017; in final form July 2, 2017; Published online July 7, 2017
Bibliographic databases:
Document Type: Article
MSC: 35Q51; 37K10; 37K15; 37K40; 39A14
Language: English
Citation: Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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