Evolution of non-stationary pulses in a cold magnetized quark-gluon plasma

Abstract

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 generalised nonlinear Schrödinger (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 numberwhere 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 initial parameters they can evolve either into the NLS envelop solitons or into dispersive wave trains.

Soliton solutions of MHD equations in cold quark gluon plasma

“…As stated before, the fundamental idea of the MIT bag model describes the QGP as an ideal gas of non-interacting quarks and gluons. Quarks move freely inside the bag to the first order of approximation while their interaction with gluons are not taken into account [12,36]. The confinement interpreted through the bag constant B bag , which is the needed energy to create a bag in the QCD vacuum.…”

“…This means that we have to apply the multi-fluid approach to set up the equations of motion [36,43,44]. The MHD equations consist of conservation equations for baryon number and the energy-momentum, in addition to Maxwell's equations [12,36,45,46]. The baryon density conservation law and Euler equations can be written as follows:…”

“…Stability and characteristics of localized waves in magnetized cold QGP also have been studied in [11,59] and [12].…”

“…It is interesting to investigate such effects on the characteristics of localized waves in QGP fluid. The evolution of arbitrary non-stationary pulses in cold QGP also has been studied in [12]. As stated before, they have derived the Ostrovsky equation for localized waves because of taking a fixed external magnetic field in the QGP and neglecting the effects of the electromagnetic field created by the QGP.…”

“…This means that quarks are very close together in a situation where the strong force becomes negligible as the constant of strong coupling α s goes toward zero [7,8], while the electromagnetic coupling constant α remainsalmost unchanged [9,10]. In such media, electromagnetic interaction plays a dominant role, and thus one can apply quantum electrodynamics version of classical mechanics together with the hydrodynamics equations [11][12][13]. Indeed, the presence of a strong magnetic field in quark stars and magnetars (as a deconfined state of mater) is due to the electromagnetic interactions.…”