  We briefly report on some exact results [G. Fiore, arXiv:1312.4665 preprint,
to appear in J. Phys. A] regarding plane waves in a relativistic cold plasma.
If the plasma, initially at rest, is reached by a transverse plane
electromagnetic travelling-wave, then its motion has a very simple dependence
on this wave in the limit of zero density, otherwise can be determined by an
iterative procedure whose accuracy decreases with time or the plasma density.
Thus one can describe in particular the impact of a very intense and short
laser pulse onto a plasma and determine conditions for the "slingshot effect"
[G. Fiore, R. Fedele, U. De Angelis, arXiv:1309.1400 preprint] to occur. The
motion in vacuum of a charged test particle subject to a wave of the same kind
is also determined, for any initial velocity.
