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

 dc.citation.epage 102710-23 en_US dc.citation.issueNumber 10 en_US dc.citation.spage 102710-1 en_US dc.citation.volumeNumber 50 en_US dc.contributor.author Habibullin, I. en_US dc.contributor.author Zheltukhina, N. en_US dc.contributor.author Pekcan, A. en_US dc.date.accessioned 2016-02-08T10:01:51Z dc.date.available 2016-02-08T10:01:51Z dc.date.issued 2009 en_US dc.department Department of Mathematics en_US dc.description.abstract We 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.doi 10.1063/1.3251334 en_US dc.identifier.issn 0022-2488 dc.identifier.uri http://hdl.handle.net/11693/22571 dc.language.iso English en_US dc.relation.isversionof http://dx.doi.org/10.1063/1.3251334 en_US dc.source.title Journal of Mathematical Physics en_US dc.title Complete list of Darboux integrable chains of the form t 1 x = t x + d ( t, t 1 ) en_US dc.type Article en_US
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