On the complete integrability of nonlinear dynamical systems on functional manifolds within the gradient-holonomic approach

DOI10.1016/S0034-4877(12)60011-1zbMath1261.37029arXiv1010.2531MaRDI QIDQ442066

Anatoliy K. Prykarpatsky, Yarema A. Prykarpatsky, Valeriy H. Samoylenko, Nikolai N. jun. Bogoliubov

Publication date: 9 August 2012

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.2531

zbMATH Keywords

nonlinear dynamical systemsLax-type representationgradient-holonomic method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)

Related Items (8)

The Bargmann type reduction for some Lax integrable two-dimensional generalization of the relativistic Toda lattice ⋮ Inverse spectral transform for the Ragnisco-Tu equation with heaviside initial condition ⋮ New integrable differential-difference and fractional nonlinear dynamical systems and their algebro-analytical properties ⋮ New fractional nonlinear integrable Hamiltonian systems ⋮ A discrete nonlinear Schrödinger-type hierarchy, its finite-dimensional reduction analysis, and the numerical integration scheme ⋮ The Ablowitz–Ladik hierarchy integrability analysis revisited: the vertex operator solution representation structure ⋮ On symmetry analysis of differential systems on functional manifolds ⋮ Discrete approximations on functional classes for the integrable nonlinear Schrödinger dynamical system: a symplectic finite-dimensional reduction approach

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