Borshch, Maxim S.; Zhdanov, Valery I. Exact solutions of the equations of relativistic hydrodynamics representing potential flows. (English) Zbl 1131.76062 SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 116, 11 p. (2007). Summary: We use a connection between relativistic hydrodynamics and scalar field theory to generate exact analytic solutions describing non-stationary inhomogeneous flows of 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. Cited in 4 Documents MSC: 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) 76M55 Dimensional analysis and similarity applied to problems in fluid mechanics Keywords:perfect fluid; one-parametric equation of state; symmetry PDFBibTeX XMLCite \textit{M. S. Borshch} and \textit{V. I. Zhdanov}, SIGMA, Symmetry Integrability Geom. Methods Appl. 3, Paper 116, 11 p. (2007; Zbl 1131.76062) Full Text: DOI arXiv EuDML EMIS