We consider Poisson bialgebras on symplectic leaves of a Poisson manifold. New classes of completely integrable Hamiltonian systems with arbitrary many degrees of freedom are presented. Their Hamiltonians are defined as the k^th coproduct of arbitrary smooth functions on symplectic foliations. We also consider modifications of the Poisson bialgebras by introducing the deformed coproduct and the deformed Poisson tensor.

PACS numbers: 02.20.Sv, 02.90.+p, 04.20.Fy