Korteveg-de Vries solitons in a cold quark-gluon plasma

Abstract

The relativistic heavy ion program developed at RHIC and now at LHC motivated a deeper study of the properties of the quark gluon plasma (QGP) and, in particular, the study of perturbations in this kind of plasma. We are interested on the time evolution of perturbations in the baryon and energy densities. If a localized pulse in baryon density could propagate throughout the QGP for long distances preserving its shape and without loosing localization, this could have interesting consequences for relativistic heavy ion physics and for astrophysics. A mathematical way to proove that this can happen is to derive (under certain conditions) from the hydrodynamical equations of the QGP a Korteveg-de Vries (KdV) equation. The solution of this equation describes the propagation of a KdV soliton. The derivation of the KdV equation depends crucially on the equation of state (EOS) of the QGP. The use of the simple MIT bag model EOS does not lead to KdV solitons. Recently we have developed an EOS for the QGP which includes both perturbative and non-perturbative corrections to the MIT one and is still simple enough to allow for analitycal manipulations. With this EOS we were able to derive a KdV equation for the cold QGP.

Shock wave formation in hot nuclear matter

“…In previous works, we have studied wave propagation in cold nuclear matter and the formation of Kortweg-de Vries solitons in non-relativistic [2] and relativistic [3,4] hydrodynamics. In [5] this study was extended to spherical geometry and finally, in [6], we have considered the problem at finite temperature. All the details and approximations involved in the derivation of the formulas presented below can be found in the mentioned works.…”

The evolution of tubular structures in a viscous quark gluon plasma

“…In most of these works [3,4] a linearized version of hydrodynamics is employed. We have tried to keep the nonlinear terms in the equations which describe the evolution of the perturbations [5,6]. This extends the validity of our formalism to perturbations which are not so small.…”

“…1. The propagation of perturbations on the top of a QGP background has been investigated in several works [3,4,5,6]. In most of these works [3,4] a linearized version of hydrodynamics is employed.…”

Dispersive Rarefaction Wave With a Large Initial Gradient

“…We emphasize that the study of analytic properties of solutions of the KdV equation and their asymptotic behavior is one of the interesting problems of the modern mathematical physics [9], [17]- [26]. It should be noted that the KdV equation remains a most important model in hydrodynamics [31] and physics of plasma up to subnuclear scales [29]. In particular, the latest research was aimed to the study of rarefaction waves [34,35].…”