Commutative Poisson subalgebras for the Sklyanin bracket and deformations of known integrable models
A hierarchy of commutative Poisson subalgebras for the Sklyanin bracket is proposed. Each of the subalgebras provides a complete set of integrals in involution with respect to the Sklyanin bracket. Using different representations of the bracket, we find some integrable models and a separation of variables for them. The models obtained are deformations of known integrable systems like the Goryachev-Chaplygin top, the Toda lattice and the Heisenberg model.
- Pub Date:
- December 2001
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- 11 pages, LaTeX with amssymb