We study magneto hydrodynamic (MHD) equations in a non-relativistic ideal and cold quark gluon plasma. We use a simple equation of state for the quark-gluon plasma (QGP) and expand the MHD equations around the system equilibrium situation. The complete set of equations shows that a magnetic field is formed in the environment due to the motion of electrically charged components. The resulting magnetic field causes to create stable solitary waves, which is governed by a modified form of the \\\'derivative nonlinear Schrodinger\\\' equation. Analytical solutions of this equation have been derived, and its characteristics are discussed. It is shown that the presence of a magnetic field stabilizes the solitary waves in such deconfined media. Dynamics and identifications of derived stable localized waves are important results that can be used in quantum plasmas, lattice QCD simulations, the evolution of nuclear matter in the form of nuclear-acoustic waves generation, excitation, wave propagation, and stability problems as well as in the evolution of super dense astrophysical objects.

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