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SIGMA, 2010, Volume 6, 034, 14 pages (Mi sigma491)  

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

The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces

Oksana Ye. Hentosh

Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 3B Naukova Str., Lviv, 79060, Ukraine

Abstract: The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a specially constructed Bäcklund transformation. The Hamiltonian description for the corresponding set of squared eigenfunction symmetry hierarchies is represented. The relation of these hierarchies with Lax integrable $(2+1)$-dimensional differential-difference systems and their triple Lax-type linearizations is analysed. The existence problem of a Hamiltonian representation for the coupled Lax-type hierarchy on a dual space to the central extension of the shift operator Lie algebra is solved also.

Keywords: Lax integrable differential-difference systems; Bäcklund transformation; squared eigenfunction symmetries

DOI: https://doi.org/10.3842/SIGMA.2010.034

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Full text: http://emis.mi.ras.ru/journals/SIGMA/2010/034/
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Bibliographic databases:

ArXiv: 1004.2945
MSC: 37J05; 37K10; 37K30; 37K35; 37K60
Received: November 16, 2009; in final form February 24, 2010; Published online April 17, 2010
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Citation: Oksana Ye. Hentosh, “The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces”, SIGMA, 6 (2010), 034, 14 pp.

Citation in format AMSBIB
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\by Oksana Ye.~Hentosh
\paper The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
\jour SIGMA
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\vol 6
\papernumber 034
\totalpages 14
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Hentosh O.E., “Lie-Algebraic Structure of the Lax-Integrable (2|1+1)-Dimensional Supersymmetric Matrix Dynamical Systems”, Ukr. Math. J., 69:10 (2018), 1537–1560  crossref  mathscinet  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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