Explicit solutions of classical generalized toda models

• DOI: 10.1007/bf01390233
• Publication Date: 2005-04-02T13:31:52Z
• Authors: M. A. Olshanetsky; A. M. Perelomov
• Keywords: Toda lattice; Matrix (chemical analysis)

The explicit solution of the generalized Toda models connected with the root systems of simple Lie algebras is constructed. This solution is obtained by a special projection of geodesic flows on some symmetric spaces on the phase space of the Toda models. In particular, for the usualN-body Toda model the solutions are expressed by minors of the exponent of the Jacobi matrix depending on initial data.