The trigonometric spin Ruijsenaars-Sutherland hierarchy is obtained by Poisson reduction of a bi-Hamiltonian free system on T*U(n), yielding explicit compatible reduced Poisson brackets.
Bihamiltonian Geometry, Darboux Coverings, and Linearization of the KP Hierarchy
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abstract
We use ideas of the geometry of bihamiltonian manifolds, developed by Gel'fand and Zakharevich, to study the KP equations. In this approach they have the form of local conservation laws, and can be traded for a system of ordinary differential equations of Riccati type, which we call the Central System. We show that the latter can be linearized by means of a Darboux covering, and we use this procedure as an alternative technique to construct rational solutions of the KP equations.
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Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$ to spin Ruijsenaars--Sutherland models
The trigonometric spin Ruijsenaars-Sutherland hierarchy is obtained by Poisson reduction of a bi-Hamiltonian free system on T*U(n), yielding explicit compatible reduced Poisson brackets.