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Preprints Archive: Abstract of IC2010091 (2010)

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On the complete integrability of nonlinear dynamical systems on discrete manifolds within the gradient-holonomic approach

by Yarema A. Prykarpatsky, Nikolai N. Bogolubov (Jr.), Anatoliy K. Prykarpatsky and Valeriy H. Samoylenko

Document info: Pages 13, Figures 0.

A gradient-holonomic approach for the Lax type integrability analysis of differential-discrete dynamical systems is devised. The asymptotical solutions to the related Lax equation are studied and the related gradient identity is stated. The integrability of a discrete nonlinear Schroedinger type dynamical system is treated in detail. The integrability of a generalized Riemann type discrete hydrodynamical system is discussed.

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