The Poisson bracket compatible with the classical reflection equation algebra

Details The Poisson bracket compatible with the classical reflection equation algebra The Poisson bracket compatible with the classical reflection equation algebra

2007-09-03

arxiv.org/abs/0709.0242v1

Regular and Chaotic Dynamics, v.13, n.3, 191-203, 2008

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, LaTeX with AmsFonts

Scientific paper

10.1134/S1560354708030052

We introduce a family of compatible Poisson brackets on the space of $2\times
2$ polynomial matrices, which contains the reflection equation algebra bracket.
Then we use it to derive a multi-Hamiltonian structure for a set of integrable
systems that includes the $XXX$ Heisenberg magnet with boundary conditions, the
generalized Toda lattices and the Kowalevski top.

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