  The relativistic heavy ion program developed at RHIC and now at LHC motivated
a deeper study of the properties of the quark gluon plasma (QGP) and, in
particular, the study of perturbations in this kind of plasma. We are
interested on the time evolution of perturbations in the baryon and energy
densities. If a localized pulse in baryon density could propagate throughout
the QGP for long distances preserving its shape and without loosing
localization, this could have interesting consequences for relativistic heavy
ion physics and for astrophysics. A mathematical way to proove that this can
happen is to derive (under certain conditions) from the hydrodynamical
equations of the QGP a Korteveg-de Vries (KdV) equation. The solution of this
equation describes the propagation of a KdV soliton. The derivation of the KdV
equation depends crucially on the equation of state (EOS) of the QGP. The use
of the simple MIT bag model EOS does not lead to KdV solitons. Recently we have
developed an EOS for the QGP which includes both perturbative and
non-perturbative corrections to the MIT one and is still simple enough to allow
for analitycal manipulations. With this EOS we were able to derive a KdV
equation for the cold QGP.
