Korteweg–de Vries solitons in relativistic hydrodynamics

Fogaça, D. A.; Navarra, F. S.

doi:10.1016/j.physletb.2007.01.001

Cited by 20 publications

(39 citation statements)

References 17 publications

(29 reference statements)

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“…Following the same formalism already used for nuclear matter in [17,18,19,20] we will now expand both (5) and (24) in powers of a small parameter σ and combine these two equations to find one single differential equation which governs the space-time evolution of the perturbation in the baryon density. We write (5) and (24) in one cartesian dimension (x) in terms of the dimensionless variables:…”

Section: Wave Equation At Zero Temperaturementioning

confidence: 99%

“…The other one is to have a third order spatial derivative term. This term comes from the equation of state of the fluid and it appears because the Lagrangian density contains higher derivative couplings [17,18,19] or because of the Laplacians appearing in the equations of motion of the fields of the theory [20]. This happens, for example, in the non-linear Walecka model of nuclear matter at zero and finite temperature.…”

Section: Introductionmentioning

confidence: 99%

“…We extended those pioneering studies to relativistic and warm nuclear matter [17,18,19,20] and now to the quark gluon plasma (QGP).…”

Section: Introductionmentioning

confidence: 99%

“…The most interesting aspect of [17,18,19,20,24,25] was to find at some point of the developement, the (KdV) equation for the perturbation in the nuclear matter density. This is the "nuclear soliton".…”

Section: Introductionmentioning

confidence: 99%

“…This is the "nuclear soliton". Our main contribution was to establish a connection between the KdV equation (and the properties of its solitonic solutions) and a modern underlying nuclear matter theory (which in our case was a variant of the non-linear Walecka model) and then to show that the soliton solution exists even in relativistic hydrodynamics [17,18].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear waves in a quark gluon plasma

2010

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Recent measurements at RHIC suggest that a nearly perfect fluid of quarks and gluons is produced in A A collisions. Moreover the passage of supersonic partons through this medium seems to produce waves. These waves might pile up and form Mach cones, which would manifest themselves in the so called away-side jets, forming a broad structure in the angular distribution of the particles recoiling against a trigger jet of moderate energy. In most of the theoretical descriptions of these phenomena, the hydrodynamic equations are linearized for simplicity. We propose an alternative explanation for the observed broadening of the away-side peak. It is based on hydrodynamics but it is a consequence of the non-linearities of the equations, which instead of simple waves may lead to localized waves or even solitons.We investigate in detail the consequences of including the non-linear terms. We use a simple equation of state for the QGP and expand the hydrodynamic equations around equilibrium configurations. The resulting differential equations describe the propagation of perturbations in the energy density. We solve them numerically and find that localized perturbations can propagate for long distances in the plasma. Under certain conditions our solutions mimick the propagation of Korteweg -de Vries solitons.

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Section: Wave Equation At Zero Temperaturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…We extended those pioneering studies to relativistic and warm nuclear matter [17,18,19,20] and now to the quark gluon plasma (QGP).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear waves in a quark gluon plasma

2010

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Possible Dark States Induced by a Surface Wave Along a Vacuum-Matter Boundary

Kwang-Hua¹

2009

Int J Theor Phys

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Possible dark states could be induced after derivations of the entrainment of matter induced by a surface wave propagating along the flexible vacuum-matter boundary by considering the nonlinear coupling between the interface and the rarefaction effect. The nonrelativistic limit of the relativistic Navier-Stokes equations was considered and analytically solved by a perturbation approach. The critical reflux values associated with the product of the second-order body forcing and the Reynolds number (representing the viscous dissipations) decrease as the Knudsen number (representing the rarefaction measure) increases from zero to 0.1. We obtained the critical bounds for possible dark states corresponding to specific Reynolds numbers (ratio of wave inertia and viscous dissipation effects) and wave numbers which might be linked to the dissipative evolution of certain large-scale structure during the relativistic heavy-ion collisions.

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Shock wave formation in hot nuclear matter

2011

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Assuming that nuclear matter can be treated as a perfect fluid, we study the propagation of perturbations in the baryon density at high temperature. The equation of state is derived from the non-linear Walecka model. The expansion of the Euler and continuity equations of relativistic hydrodynamics around equilibrium configurations lead to the breaking wave equation for the density perturbation. We solve it numerically for this perturbation and follow the propagation of the initial pulses.

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Korteweg–de Vries solitons in relativistic hydrodynamics

Cited by 20 publications

References 17 publications

Nonlinear waves in a quark gluon plasma

Nonlinear waves in a quark gluon plasma

Possible Dark States Induced by a Surface Wave Along a Vacuum-Matter Boundary

Shock wave formation in hot nuclear matter

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