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SIGMA, 2017, Volume 13, 053, 14 pages (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

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.


DOI: https://doi.org/10.3842/SIGMA.2017.053

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Bibliographic databases:

Document Type: Article
MSC: 35Q51; 37K10; 37K15; 37K40; 39A14
Received: March 31, 2017; in final form July 2, 2017; Published online July 7, 2017
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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    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. Runliang Lin, Yukun Du, “Generalized Darboux transformation for the discrete Kadomtsev–Petviashvili equation with self-consistent sources”, Theoret. and Math. Phys., 196:3 (2018), 1320–1332  mathnet  crossref  crossref  adsnasa  isi  elib
    2. R. Ch. Kulaev, A. K. Pogrebkov, A. B. Shabat, “Darboux system as three-dimensional analog of Liouville equation”, Russian Mathematics, 62:12 (2018), 50–58  mathnet  crossref  isi
    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. R. Ch. Kulaev, A. K. Pogrebkov, A. B. Shabat, “Darboux system: Liouville reduction and an explicit solution”, Proc. Steklov Inst. Math., 302 (2018), 250–269  mathnet  crossref  crossref  isi  elib
    5. Pogrebkov A., “Hirota Difference Equation and Darboux System: Mutual Symmetry”, Symmetry-Basel, 11:3 (2019), 436  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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