  We study Lie-Poisson actions on symplectic manifolds. We show that they are
generated by non-Abelian Hamiltonians. We apply this result to the group of
dressing transformations in soliton theories; we find that the non-Abelian
Hamiltonian is just the monodromy matrix. This provides a new proof of their
Lie-Poisson property. We show that the dressing transformations are the
classical precursors of the non-local and quantum group symmetries of these
theories. We treat in detail the examples of the Toda field theories and the
Heisenberg model.
