  Relativistic electromagnetic plasma waves are described by a dynamical
equation that can be solved not only in terms of plane waves, but for several
different accelerating wavepacket solutions. Depending on the spatial and
temporal dependence of the plasma frequency, different kinds of accelerating
solution can be obtained, for example, in terms of Airy or Weber functions.
Also, we show that an arbitrary accelerated wavepacket solution is possible,
for example, for a system with a luminal plasma slab.
