Opuscula Math. 32, no. 1 (2012), 41-66
Isospectral integrability analysis of dynamical systems on discrete manifolds
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.