A family of the Poisson brackets compatible with the Sklyanin bracket

Abstract

We introduce a family of compatible Poisson brackets on the space of $2\times 2$ polynomial matrices, which contains the Sklyanin bracket, and use it to derive a multi-Hamiltonian structure for a set of integrable systems that includes $XXX$ Heisenberg magnet, the open and periodic Toda lattices, the discrete self-trapping model and the Goryachev-Chaplygin gyrostat.

16 pages, LaTeX with Amsfonts; corrected typos

References in corpus (1)

• On the Darboux-Nijenhuis Variables for the Open Toda Lattice

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