  We study weakly nonlinear wave perturbations propagating in a cold
nonrelativistic and magnetized ideal quark-gluon plasma. We show that such
perturbations can be described by the Ostrovsky equation. The derivation of
this equation is presented for the baryon density perturbations. Then we show
that the generalized nonlinear Schr{\"o}dinger (NLS) equation can be derived
from the Ostrovsky equation for the description of quasi-harmonic wave trains.
This equation is modulationally stable for the wave number $k < k_m$ and
unstable for $k > k_m$, where $k_m$ is the wave number where the group velocity
has a maximum. We study numerically the dynamics of initial wave packets with
the different carrier wave numbers and demonstrate that depending on the
initial parameters they can evolve either into the NLS envelope solitons or
into dispersive wave trains.
