  The nonlinear interaction, due to quantum electrodynamical (QED) effects,
between an electromagnetic pulse and a radiation background is investigated, by
combining the methods of radiation hydrodynamics with the QED theory for
photon-photon scattering. For the case of a single coherent electromagnetic
pulse we obtain a Zakharov-like system, where the radiation pressure of the
pulse acts as a driver of acoustic waves in the photon gas. For a sufficiently
intense pulse and/or background energy density there is focusing and subsequent
collapse of the pulse. The relevance of our results for various astrophysical
applications are discussed.
