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dc.contributor.authorHabibullin, I.en_US
dc.contributor.authorZheltukhina, N.en_US
dc.contributor.authorSakieva, A.en_US
dc.date.accessioned2016-02-08T09:56:22Z
dc.date.available2016-02-08T09:56:22Z
dc.date.issued2010en_US
dc.identifier.issn17518113
dc.identifier.urihttp://hdl.handle.net/11693/22164
dc.description.abstractA differential-difference equation d/dx t(n + 1, x) = f (x, t(n, x), t(n + 1, x), d/dx t(n, x)) with unknown t(n, x) depending on the continuous and discrete variables x and n is studied. We call an equation of such kind Darboux integrable if there exist two functions (called integrals) F and I of a finite number of dynamical variables such that DxF = 0 and DI = I, where Dx is the operator of total differentiation with respect to x and D is the shift operator: Dp(n) = p(n + 1). It is proved that the integrals can be brought to some canonical form. A method of construction of an explicit formula for a general solution to Darboux-integrable chains is discussed and such solutions are found for a class of chains. © 2010 IOP Publishing Ltd.en_US
dc.language.isoEnglishen_US
dc.source.titleJournal of Physics A: Mathematical and Theoreticalen_US
dc.relation.isversionofhttp://dx.doi.org/10.1088/1751-8113/43/43/434017en_US
dc.titleOn Darboux-integrable semi-discrete chainsen_US
dc.typeArticleen_US
dc.departmentDepartment of Mathematicsen_US
dc.citation.spage434017en_US
dc.citation.volumeNumber43en_US
dc.citation.issueNumber43en_US
dc.identifier.doi10.1088/1751-8113/43/43/434017en_US


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