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Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of the perfect fluid with one-parametric equation of state (EOS) $p=p(\varepsilon)$. For linear EOS $p=\kappa\varepsilon$ we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS ($\kappa=1$) we obtain "monopole $+$ dipole" and "monopole $+$ quadrupole" axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.
Keywords: relativistic hydrodynamics; exact solutions. 
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Maxim S. Borshch; Valery I. Zhdanov. Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a115/

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