Isospectral integrability analysis of dynamical systems on discrete manifolds

Denis Blackmore, Anatoliy K. Prykarpatsky, Yarema A. Prykarpatsky

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)41-66
Number of pages26
JournalOpuscula Mathematica
Volume32
Issue number1
DOIs
StatePublished - 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Asymptotic analysis
  • Conservation laws
  • Finite-dimensional reduction
  • Gradient holonomic algorithm
  • Lax representation
  • Liouville integrability
  • Nonlinear discrete dynamical systems
  • Poissonian structures

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