Isospectral integrability analysis of dynamical systems on discrete manifolds

Denis Blackmore , Anatolij K. Prykarpatsky , Yarema A. Prykarpatskyy

Abstract

It is shown how functional-analytic gradient-holonomic structures can be used for an isospectral integrability analysis of nonlinear dynamical systems on discrete manifolds. The approach developed is applied to obtain detailed proofs of the integrability of the discrete nonlinear Schrödinger, Ragnisco-Tu and Riemann-Burgers dynamical systems.
Author Denis Blackmore
Denis Blackmore,,
-
, Anatolij K. Prykarpatsky
Anatolij K. Prykarpatsky,,
-
, Yarema A. Prykarpatskyy (FoEEaLS / DoAM)
Yarema A. Prykarpatskyy,,
- Department of Applied Mathematics
Journal seriesOpuscula Mathematica, ISSN 1232-9274, e-ISSN 2300-6919, (B 9 pkt)
Issue year2012
Vol32
No1
Pages41-66
Publication size in sheets2.05
Keywords in EnglishGradient holonomic algorithm, conservation laws, asymptotic analysis, Poissonian structures, Lax representation, finite-dimensional reduction, Liouville integrability, nonlinear discrete dynamical systems
ASJC Classification2600 General Mathematics
DOIDOI:10.7494/OpMath.2012.32.1.41
URL https://www.opuscula.agh.edu.pl/vol32/1/art/opuscula_math_3204.pdf
Languageen angielski
Score (nominal)9
Score sourcejournalList
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2013 = 0.222
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