On Darboux-integrable semi-discrete chains
dc.citation.issueNumber | 43 | en_US |
dc.citation.spage | 434017 | en_US |
dc.citation.volumeNumber | 43 | en_US |
dc.contributor.author | Habibullin, I. | en_US |
dc.contributor.author | Zheltukhina, N. | en_US |
dc.contributor.author | Sakieva, A. | en_US |
dc.date.accessioned | 2016-02-08T09:56:22Z | |
dc.date.available | 2016-02-08T09:56:22Z | |
dc.date.issued | 2010 | en_US |
dc.department | Department of Mathematics | en_US |
dc.description.abstract | A 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.identifier.doi | 10.1088/1751-8113/43/43/434017 | en_US |
dc.identifier.issn | 17518113 | |
dc.identifier.uri | http://hdl.handle.net/11693/22164 | |
dc.language.iso | English | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1088/1751-8113/43/43/434017 | en_US |
dc.source.title | Journal of Physics A: Mathematical and Theoretical | en_US |
dc.title | On Darboux-integrable semi-discrete chains | en_US |
dc.type | Article | en_US |
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