Complete list of Darboux integrable chains of the form t 1 x = t x + d ( t, t 1 )

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dc.citation.epage102710-23en_US
dc.citation.issueNumber10en_US
dc.citation.spage102710-1en_US
dc.citation.volumeNumber50en_US
dc.contributor.authorHabibullin, I.en_US
dc.contributor.authorZheltukhina, N.en_US
dc.contributor.authorPekcan, A.en_US
dc.date.accessioned2016-02-08T10:01:51Z
dc.date.available2016-02-08T10:01:51Z
dc.date.issued2009en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractWe study differential-difference equation (d/dx) t (n+1,x) =f (t (n,x),t (n+1,x), (d/dx) t (n,x)) with unknown t (n,x) depending on continuous and discrete variables x and n. Equation of such kind is called Darboux integrable, if there exist two functions F and I of a finite number of arguments x, { t (n+k,x) } k=-∞ ∞, {(dk /d xk) t (n,x) } k=1 ∞, such that Dx F=0 and DI=I, where D x is the operator of total differentiation with respect to x and D is the shift operator: Dp (n) =p (n+1). Reformulation of Darboux integrability in terms of finiteness of two characteristic Lie algebras gives an effective tool for classification of integrable equations. The complete list of Darboux integrable equations is given in the case when the function f is of the special form f (u,v,w) =w+g (u,v). © 2009 American Institute of Physics.en_US
dc.identifier.doi10.1063/1.3251334en_US
dc.identifier.issn0022-2488
dc.identifier.urihttp://hdl.handle.net/11693/22571
dc.language.isoEnglishen_US
dc.relation.isversionofhttp://dx.doi.org/10.1063/1.3251334en_US
dc.source.titleJournal of Mathematical Physicsen_US
dc.titleComplete list of Darboux integrable chains of the form t 1 x = t x + d ( t, t 1 )en_US
dc.typeArticleen_US
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