Bi-Hamiltonian ordinary differential equations with matrix variables
Abstract
We consider a special class of Poisson brackets related to systems of ordinary differential equations with matrix variables. We investigate general properties of such brackets, present an example of a compatible pair of quadratic and linear brackets, and find the corresponding hierarchy of integrable models, which generalizes the two-component Manakov matrix system to the case of an arbitrary number of matrices.
- Publication:
-
Theoretical and Mathematical Physics
- Pub Date:
- April 2012
- DOI:
- 10.1007/s11232-012-0043-4
- Bibcode:
- 2012TMP...171..442O
- Keywords:
-
- integrable ordinary differential equation with matrix unknowns;
- bi-Hamiltonian formalism;
- Manakov model