  The lattice Hamiltonian method is developed for solving the Vlasov equation
with nuclear mean-field based on the Skyrme pseudopotential up to
next-to-next-to-next-to leading order. The ground states of nuclei are obtained
through varying the total energy with respect to the density distribution of
nucleons. Owing to the self-consistent treatment of initial nuclear ground
state and the exact energy conservation in the lattice Hamiltonian method, the
present framework of solving the Vlasov equation exhibits very stable nuclear
ground state evolution. As a first application of the new lattice Hamiltonian
Vlasov method, we explore the iso-scalar giant monopole and iso-vector giant
dipole modes of finite nuclei. The obtained results are shown to be comparable
to that from random-phase approximation and consistent with the experimental
data, indicating the capability of the present method in dealing with the
long-time near-equilibrium nuclear dynamics.
