Browsing by Subject "Toda lattice"
Now showing items 19 of 9

Article
BogoyavlenskyVolterra and Birkhoff integrable systems
(2004)In this paper we examine an interesting connection between the generalized Volterra lattices of Bogoyavlensky and a special case of an integrable system defined by Sklyanin. The Sklyanin system happens to be one of the ...

Article
The modular hierarchy of the Toda lattice
(2007)The modular vector field plays an important role in the theory of Poisson manifolds and is intimately connected with the Poisson cohomology of the space. In this paper we investigate its significance in the theory of ...

Article
Multiple Hamiltonian structure of BogoyavlenskyToda lattices
(2004)This paper is mainly a review of the multiHamiltonian nature of Toda and generalized Toda lattices corresponding to the classical simple Lie groups but it includes also some new results. The areas investigated include ...

Article
The negative Toda hierarchy and rational Poisson brackets
(2003)In this paper we extend the usual hierarchies for the finite, nonperiodic Toda lattice for negative values of the index. We define an infinite sequence of rational homogeneous Poisson brackets, master symmetries, invariants ...

Article
Noether and master symmetries for the Toda lattice
(2005)In this letter we examine the interrelation between Noether symmetries, master symmetries and recursion operators for the Toda lattice. The topics include invariants, higher Poisson brackets and the various relations they ...

Article
On generalized Volterra systems
(2015)We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The algorithm uses the root system of a complex simple Lie algebra. The Hamiltonian vector field is ...

Article
Reduction and realization in toda and volterra
(2008)We construct a new symplectic, biHamiltonian realization of the KMsystem by reducing the corresponding one for the Toda lattice. The biHamiltonian pair is constructed using a reduction theorem of Fernandes and Vanhaecke. ...

Article
So (p, q) Toda systems
(2013)We define an integrable Hamiltonian system of Toda type associated with the real Lie algebra so(p,q). As usual there exist a periodic and a nonperiodic version. We construct, using the root space, two Lax pair representations ...

Article
The Toda lattice is superintegrable
(2006)We prove that the classical, nonperiodic Toda lattice is superintegrable. In other words, we show that it possesses 2 N  1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient ...