Isospectral integrability analysis of dynamical systems on discrete manifolds

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

doi:10.7494/OpMath.2012.32.1.41

Isospectral integrability analysis of dynamical systems on discrete manifolds

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

Mathematical Sciences

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	41-66
Number of pages	26
Journal	Opuscula Mathematica
Volume	32
Issue number	1
DOIs	https://doi.org/10.7494/OpMath.2012.32.1.41
State	Published - 2012

All Science Journal Classification (ASJC) codes

General Mathematics

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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10.7494/OpMath.2012.32.1.41

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AB - 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.

KW - Asymptotic analysis

KW - Conservation laws

KW - Finite-dimensional reduction

KW - Gradient holonomic algorithm

KW - Lax representation

KW - Liouville integrability

KW - Nonlinear discrete dynamical systems

KW - Poissonian structures

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Isospectral integrability analysis of dynamical systems on discrete manifolds

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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