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Ufimsk. Mat. Zh., 2011, Volume 3, Issue 1, Pages 80–84 (Mi ufa83)  

This article is cited in 2 scientific papers (total in 2 papers)

Necessary conditions of Darboux integrability for differential-difference equations of a special kind

S. Ya. Startsev

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia

Abstract: This work dwells upon chains of differential equations of the form $\varphi(x,u_{i+1},(u_{i+1})_x)=\psi(x,u_i,(u_i)_x)$, where $u$ depends on the discrete variable $i$ and the continuous variable $x$, and the functions $\varphi(x,y,z)$, $\psi(x,y,z)$ and $x$ are functionally-independent. We demonstrate that necessary Darboux integrability conditions for chains of the above form can be easily derived from already known results. These conditions are not sufficient but may be useful for classification of Darboux-integrable differential-difference equations. As an auxiliary result, we also prove a proposition about structure of symmetries for differential-difference equations of a more general form.

Keywords: Darboux integrability, differential-difference equations.

Full text: PDF file (357 kB)
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English version:
Ufa Mathematical Journal, 2011, 3:1, 78–82 (PDF, 343 kB)

Bibliographic databases:
UDC: 517.929
Received: 25.10.2010

Citation: S. Ya. Startsev, “Necessary conditions of Darboux integrability for differential-difference equations of a special kind”, Ufimsk. Mat. Zh., 3:1 (2011), 80–84; Ufa Math. J., 3:1 (2011), 78–82

Citation in format AMSBIB
\Bibitem{Sta11}
\by S.~Ya.~Startsev
\paper Necessary conditions of Darboux integrability for differential-difference equations of a~special kind
\jour Ufimsk. Mat. Zh.
\yr 2011
\vol 3
\issue 1
\pages 80--84
\mathnet{http://mi.mathnet.ru/ufa83}
\zmath{https://zbmath.org/?q=an:1240.34025}
\transl
\jour Ufa Math. J.
\yr 2011
\vol 3
\issue 1
\pages 78--82


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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. S. Ya. Startsev, “Integriruemye po Darbu differentsialno-raznostnye uravneniya, dopuskayuschie integral pervogo poryadka”, Ufimsk. matem. zhurn., 4:3 (2012), 161–176  mathnet
    2. S. Ya. Startsev, “Darboux integrable discrete equations possessing an autonomous first-order integral”, J. Phys. A, 47:10 (2014), 105204, 16 pp.  crossref  mathscinet  zmath  isi  elib  scopus
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