we derive equations of motion for the coupled Bogoliubov quasiparticle-phonon system treating the phonons at a fully quantum kinetic level. The pump-pulse-induced dynamics of this model is investigated in the collisionless regime, i.e., at time scales shorter than the quasiparticle relaxation time, for which BCS mean-field theory is applicable [@volkov1974; @YuzJofPhys05]. The pump-probe experiments of Matsunaga *et al.* [@matsunagaPRL12; @matsunagaPRL13] have shown that in Nb$_{1-x}$Ti$_x$N thin films this collisionless regime lasts up to $10$ ps, considerably longer than the period of the order parameter oscillations, which is of the order of $1$ ps.

We study different hierarchies of the involved time scales, focusing for the most part on the case where the pump-pulse length $\tau_{\textrm{p}}$ is much shorter than both the phonon period $\tau_{\textrm{ph}} = ( 2 \pi ) / \omega_{\textrm{ph}} $ and the dynamical time scale of the superconductor $\tau_{\Delta}  \approx h / ( 2 | \Delta | ) $. In this regime, both the phononic and quasiparticle subsystems evolve in a nonadiabatic fashion, leading to order-parameter oscillations and the creation of coherent phonons. We present a detailed analysis of the generic features in the pump-probe response resulting from these oscillatory behaviors. In particular, it is shown that the 