  The dynamics of the collective excitations of a lattice Bose gas at zero
temperature is systematically investigated using the time-dependent Gutzwiller
mean-field approach. The excitation modes are determined within the framework
of the linear-response theory as solutions of the generalized Bogoliubov-de
Gennes equations valid in the superfluid and Mott-insulator phases at arbitrary
values of parameters. The expression for the sound velocity derived in this
approach coincides with the hydrodynamic relation. We calculate the transition
amplitudes for the excitations in the Bragg scattering process and show that
the higher excitation modes give significant contributions. We simulate the
dynamics of the density perturbations and show that their propagation velocity
in the limit of week perturbation is satisfactorily described by the
predictions of the linear-response analysis.
