Abstract
Simple, self-similar, analytic solutions of (1+1)-dimensional relativistic hydrodynamics are presented, generalizing the Hwa–Bjorken boost-invariant solution to inhomogeneous rapidity distributions. These solutions are generalized also to (1+3)-dimensional, cylindrically symmetric firetubes, corresponding to central collisions of heavy ions at relativistic bombarding energies.
Highlights
Analytic solution of the equations of relativistic hydrodynamics is a difficult task because the equations are non-linear partial differential equations, that are rather complicated to handle analytically and numerically.relativistic hydrodynamics has various applications, including the calculations of single-particle spectra and two-particle correlations in relativistic heavy ion collisions, see ref [1]
We present an analytic approach, which goes back to the data-motivated exact analytic solution of non-relativistic hydrodynamics found by Zimanyi, Bondorf and Garpman (ZBG) in 1978 for low energy heavy ion collisions with spherical symmetry [13]
We have found a new family of both 1+1 dimensional, longitudinally expanding, and 1+3 dimensional, cylindrically symmetric, adiabatic solutions of relativistic hydrodynamics with conserved particle number
Summary
Analytic solution of the equations of relativistic hydrodynamics is a difficult task because the equations are non-linear partial differential equations, that are rather complicated to handle analytically and numerically. We present an analytic approach, which goes back to the data-motivated exact analytic solution of non-relativistic hydrodynamics found by Zimanyi, Bondorf and Garpman (ZBG) in 1978 for low energy heavy ion collisions with spherical symmetry [13]. This solution has been extended to the case of elliptic symmetry by Zimanyi and collaborators in ref. An analytic approach, the Buda-Lund (BL) model has been developed to parameterize the single particle spectra and the two-particle Bose-Einstein correlations in high-energy heavy-ion physics in terms of hydrodynamically expanding, cylindrically symmetric sources [22].
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