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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 3, Pages 161–176 (Mi ufa160)  

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

Darboux integrable differential-difference equations admitting a firts-order integral

S. Ya. Startsev

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

Abstract: We obtain a classification of Liouville-type differential-difference equations that admit a first-order integral with respect to one of the characteristics. This classification gives us the complete description of difference substitutions which are applicable to wide classes of differential-difference evolution equations. The classification also allows us to construct the complete list of Darboux integrable differential-difference equations which admit both a second-order integral with respect to one of the characteristics and a non-point invertible transformation with respect to the same characteristic.

Keywords: Darboux integrability, differential-difference equations, difference substititions.

Full text: PDF file (614 kB)
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UDC: 517.929
Received: 21.05.2012

Citation: S. Ya. Startsev, “Darboux integrable differential-difference equations admitting a firts-order integral”, Ufimsk. Mat. Zh., 4:3 (2012), 161–176

Citation in format AMSBIB
\Bibitem{Sta12}
\by S.~Ya.~Startsev
\paper Darboux integrable differential-difference equations admitting a~firts-order integral
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 3
\pages 161--176
\mathnet{http://mi.mathnet.ru/ufa160}


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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, “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
    2. S. Ya. Startsev, “Relationships Between Symmetries Depending on Arbitrary Functions and Integrals of Discrete Equations”, J. Phys. A-Math. Theor., 50:50 (2017), 50LT01  crossref  mathscinet  zmath  isi  scopus
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