  Linear-response time-dependent density-functional theory (TDDFT) can describe
excitonic features in the optical spectra of insulators and semiconductors,
using exchange-correlation (xc) kernels behaving as $-1/k^{2}$ to leading
order. We show how excitons can be modeled in real-time TDDFT, using an xc
vector potential constructed from approximate, long-range corrected xc kernels.
We demonstrate for various materials that this real-time approach is consistent
with frequency-dependent linear response, gives access to femtosecond exciton
dynamics following short-pulse excitations, and can be extended with some
caution into the nonlinear regime.
