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
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.
Darboux integrability, differential-difference equations, difference substititions.
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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
\paper Darboux integrable differential-difference equations admitting a~firts-order integral
\jour Ufimsk. Mat. Zh.
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This publication is cited in the following articles:
S. Ya. Startsev, “Darboux integrable discrete equations possessing an autonomous first-order integral”, J. Phys. A, 47:10 (2014), 105204, 16 pp.
S. Ya. Startsev, “Relationships Between Symmetries Depending on Arbitrary Functions and Integrals of Discrete Equations”, J. Phys. A-Math. Theor., 50:50 (2017), 50LT01
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