Darboux-integrable discrete systems |
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Authors: | V L Vereshchagin |
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Institution: | (1) Institute for Mathematics and Computing Center, Urals Science Center, RAS, Ufa, Russia |
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Abstract: | We extend Laplace’s cascade method to systems of discrete “hyperbolic” equations of the form ui+1,j+1
= f(ui+1,j, ui,j+1
, ui,j), where uij is a member of a sequence of unknown vectors, i, j ∊ ℤ. We introduce the notion of a generalized Laplace invariant and the
associated property of the system being “Liouville.” We prove several statements on the well-definedness of the generalized
invariant and on its use in the search for solutions and integrals of the system. We give examples of discrete Liouville-type
systems.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 207–219, August, 2008. |
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Keywords: | Laplace’ s cascade method Darboux integrability nonlinear chain |
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