Opuscula Math. 32, no. 1 (2012), 41-66

Opuscula Mathematica

Isospectral integrability analysis of dynamical systems on discrete manifolds

Denis Blackmore
Anatoliy K. Prykarpatsky
Yarema A. Prykarpatsky

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.

Keywords: gradient holonomic algorithm, conservation laws, asymptotic analysis, Poissonian structures, Lax representation, finite-dimensional reduction, Liouville integrability, nonlinear discrete dynamical systems.

Mathematics Subject Classification: 35A30, 35G25, 35N10, 37K35, 58J70, 58J72, 34A34.

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  • Denis Blackmore
  • Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
  • Anatoliy K. Prykarpatsky
  • AGH University of Science and Technology, Faculty of Mining Surveying and Environmental Engineering, al. Mickiewicza, 30-059 Krakow, Poland
  • The Ivan Franko State Pedagogical University, Drohobych, Lviv region 82100, Ukraine
  • Yarema A. Prykarpatsky
  • Institute of Mathematics of NAS, Kyiv, Ukraine
  • The Ivan Franko State Pedagogical University, Drohobych, Lviv region, 82100, Ukraine
  • The Agrarian University of Krakow, Department of Applied Mathematics, ul. Balicka 253c, 30-198 Krakow, Poland
  • Received: 2011-01-15.
  • Revised: 2011-03-13.
  • Accepted: 2011-03-17.
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Cite this article as:
Denis Blackmore, Anatoliy K. Prykarpatsky, Yarema A. Prykarpatsky, Isospectral integrability analysis of dynamical systems on discrete manifolds, Opuscula Math. 32, no. 1 (2012), 41-66, http://dx.doi.org/10.7494/OpMath.2012.32.1.41

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