  The nonlinear interaction, due to quantum electrodynamical (QED) effects,
between photons is investigated using a wave-kinetic description. Starting from
a coherent wave description, we use the Wigner transform technique to obtain a
set of wave-kinetic equations, the so called Wigner-Moyal equations. These
equations are coupled to a background radiation fluid, whose dynamics is
determined by an acoustic wave equation. In the slowly varying acoustic limit,
we analyse the resulting system of kinetic equations, and show that they
describe instabilities, as well as Landau-like damping. The instabilities may
lead to break-up and focusing of ultra-high intensity multi-beam systems, which
in conjunction with the damping may result in stationary strong field
structures. The results could be of relevance for the next generation of
laser-plasma systems.
