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

TL;DR

This paper investigates the evolution of weakly nonlinear, non-stationary pulses in a cold, magnetized quark-gluon plasma, deriving equations that describe their behavior and stability, and demonstrating different wave evolutions through numerical simulations.

Contribution

It derives the Ostrovsky and generalized nonlinear Schrödinger equations for wave perturbations in a magnetized quark-gluon plasma, revealing their stability properties and wave evolution scenarios.

Findings

The Ostrovsky equation describes wave perturbations in the plasma.

The generalized NLS equation is modulationally stable for k < k_m.

Wave packets evolve into solitons or dispersive waves depending on initial conditions.

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 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.