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Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions

Kindybaliuk A., Prytula M.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 3

85--99

In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.

Isospectral integrability analysis of dynamical systems on discrete manifolds

Blackmore D., Prykarpatsky A. K., Prykarpatsky Y. A.

Opuscula Mathematica

2012

Vol. 32, no. 1

41-66

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.