Multiple Hamiltonian Structures for Toda-type systems

Abstract

Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas investigated, include master symmetries, recursion operators, higher Poisson brackets, invariants, and group symmetries for the systems. A survey of previous work on the classical Toda lattice is also included.

48 pages, 46 references. arXiv admin note: substantial text overlap with arXiv:nlin/0608018

References in corpus (1)

• Symmetries of Toda Equations

Cited by in corpus (13)

• A new integrable system related to the Toda lattice
• The Toda lattice is super-integrable
• From the Toda Lattice to the Volterra lattice and back
• Separation of variables in the Jacobi identities
• Multiple Hamiltonian structure of Bogoyavlensky-Toda lattices
• New solution family of the Jacobi equations: Characterization, invariants, and global Darboux analysis
• Poisson Structures of Calogero-Moser and Ruijsenaars-Schneider Models
• New four-dimensional solutions of the Jacobi equations for Poisson structures
• A symplectic realization of the Volterra lattice
• The last integrable case of kozlov-Treshchev Birkhoff integrable potentials
• Reduction and Realization in Toda and Volterra
• so(p,q) Toda Systems
• The Toda${}_2$ chain