Abstract:
We construct a new symplectic, bi-Hamiltonian realization of the KM-system by reducing the corresponding one for the Toda lattice. The bi-Hamiltonian pair is constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper we also review the important work of Moser on the Toda and KM-systems.
\Bibitem{Dam08}
\by P.~A.~Damianou
\paper Reduction and realization in Toda and Volterra
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 6
\pages 572--587
\mathnet{http://mi.mathnet.ru/rcd602}
\crossref{https://doi.org/10.1134/S1560354708060075}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2465725}
\zmath{https://zbmath.org/?q=an:1229.37061}
Linking options:
https://www.mathnet.ru/eng/rcd602
https://www.mathnet.ru/eng/rcd/v13/i6/p572
This publication is cited in the following 2 articles:
Tobias Sutter, Debasish Chatterjee, Federico A. Ramponi, John Lygeros, “Isospectral flows on a class of finite-dimensional Jacobi matrices”, Systems & Control Letters, 62:5 (2013), 388
Benito Hernández-Bermejo, “New global solutions of the Jacobi partial differential equations”, Physica D: Nonlinear Phenomena, 241:7 (2012), 764
Citation in format AMSBIB
Contact us: