Article
Ufa Mathematical Journal
Volume 4, Number 3, pp. 159-173
Darboux integrable differential-difference equations admitting a firts-order integral.
Startsev S.Ya.
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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.