On the Complete Integrability of Nonlinear Dynamical Systems on Functional Manifolds Within the Gradient-Holonomic Approach

Yarema A. Prykarpatskyy , N.N. Bogolubov , Anatolij K. Prykarpatsky , Samoy , Valeriy H. Samoylenko

Abstract

A gradient-holonomic approach for the Lax-type integrability analysis of differential-discrete dynamical systems is described. The asymptotic solutions to the related Lax equation are studied, the related gradient identity subject to its relationship to a suitable Lax-type spectral problem is analyzed in detail. The integrability of the discrete nonlinear Schrödinger, Ragnisco–Tu and Burgers–Riemann type dynamical systems is treated, in particular, their conservation laws, compatible Poissonian structures and discrete Lax-type spectral problems are obtained within the gradient-holonomic approach.
Author Yarema A. Prykarpatskyy (FoEEaLS / DoAM)
Yarema A. Prykarpatskyy,,
- Department of Applied Mathematics
, N.N. Bogolubov
N.N. Bogolubov,,
-
, Anatolij K. Prykarpatsky
Anatolij K. Prykarpatsky,,
-
, Samoy
Samoy,,
-
, Valeriy H. Samoylenko
Valeriy H. Samoylenko,,
-
Journal seriesReports on Mathematical Physics, ISSN 0034-4877, (A 20 pkt)
Issue year2011
Vol68
No3
Pages289-318
Publication size in sheets1
Keywords in EnglishGradient-holonomic method conservation laws asymptotical analysis Poissonian structures Lax-type representation finite-dimensional reduction Liouville integrability
ASJC Classification2610 Mathematical Physics; 3109 Statistical and Nonlinear Physics
DOIDOI:10.1016/S0034-4877(12)60011-1
URL https://www.sciencedirect.com/science/article/pii/S0034487712600111/pdfft?md5=9dee1445b207bba3aae503b416b2bf70&pid=1-s2.0-S0034487712600111-main.pdf
Languageen angielski
Score (nominal)20
Score sourcejournalList
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2011 = 0.645; WoS Impact Factor: 2011 = 0.643 (2) - 2011=0.627 (5)
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