  We consider a weakly interacting uniform atomic Bose gas with a
time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov
treatment we investigate the time evolution of several observables, including
the momentum distribution, the degree of coherence in the system, and their
dependence on dimensionality and temperature. We rigorously prove that the
low-momentum Bogoliubov modes remain frozen during the whole evolution, while
the high-momentum ones adiabatically follow the change in time of the
interaction strength. At intermediate momenta we point out the occurrence of
oscillations, which are analogous to Sakharov oscillations. We identify two
wide classes of time-dependent behaviors of the coupling for which an exact
solution of the problem can be found, allowing for an analytic computation of
all the relevant observables. A special emphasis is put on the study of the
coherence property of the system in one spatial dimension. We show that the
system exhibits a smooth "light-cone effect," with typically no
prethermalization.
