  A class of radiative solutions of Einstein's field equations with a negative
cosmological constant and a pure radiation is investigated. The space-times,
which generalize the Defrise solution, represent exact gravitational waves
which interact with null matter and propagate in the anti-de Sitter universe.
Interestingly, these solutions have homogeneous and non-singular wave-fronts
for all freely moving observers. We also study properties of sandwich and
impulsive waves which can be constructed in this class of space-times.
