  Pump-probe experiments have turned out as a powerful tool in order to study
the dynamics of competing orders in a large variety of materials. The
corresponding analysis of the data often relies on standard linear-response
theory generalized to non-equilibrium situations. Here we examine the validity
of such an approach within the attractive Hubbard model for which the dynamics
of pairing and charge-density wave orders is computed using the time-dependent
Hartree-Fock approximation (TDHF). Our calculations reveal that the
`linear-response assumption' is justified for small to moderate non-equilibrium
situations (i.e., pump pulses) when the symmetry of the pump-induced state
differs from that of the external field. This is the case, when we consider the
pairing response in a charge-ordered state or the charge-order response in a
superconducting state. The situation is very different when the non-equilibrium
state and the external probe field have the same symmetry. In this case, we
observe significant changes of the response in magnitude but also due to mode
coupling when moving away from an equilibrium state, indicating the failure of
the linear-response assumption.
