  We define partial differential (PD in the following), i.e., field theoretic
analogues of Hamiltonian systems on abstract symplectic manifolds and study
their main properties, namely, PD Hamilton equations, PD Noether theorem, PD
Poisson bracket, etc.. Unlike in standard multisymplectic approach to
Hamiltonian field theory, in our formalism, the geometric structure
(kinematics) and the dynamical information on the "phase space" appear as just
different components of one single geometric object.
