Classical Poisson structures and r - matrices from constrained flows
نویسندگان
چکیده
We construct the classical Poisson structure and r-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the r-matrices associated with the constrained flows of the Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a 2-dimensional eigenvalue problem. Some of the obtained r-matrices depend only on the spectral parameters, but others depend also on the dynamical variables. For consistency they have to obey a classical Yang-Baxter-type equations, possibly with dynamical extra terms. ∗permanent address of Yunbo Zeng.
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