  By means of magnetohydrodynamic equations in a non relativistic multi fluid
framework, we study the behavior of small amplitude perturbations in cold Quark
Gluon Plasmas (QGP). Magnetohydrodynamic equations, along with the QGP equation
of state are expanded using the reductive perturbation method. It is shown that
such a medium should be considered as multi fluid magnetohydrodynamic (MHD)
system. The result is a nonlinear wave equation which complies with a modified
form of the "derivative nonlinear Schrodinger" equation instead of the KdV
equation. We show that the complete set of equations, by considering the
magnetic field which is supported by the Maxwell's equations, create stable
solitary waves. An interesting result is the existence of an electric field
component along the direction of magnetic field which causes charge
separability in the medium. Properties of this solitonic solution is studied by
considering different values for the QGP characters such as background mass
density and strength of the magnetic field (at the scale of compact stars).
