Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 116, 11 pages      arXiv:0709.1053      http://dx.doi.org/10.3842/SIGMA.2007.116
Contribution to the Proceedings of the Seventh International Conference Symmetry in Nonlinear Mathematical Physics

Exact Solutions of the Equations of Relativistic Hydrodynamics Representing Potential Flows

Maxim S. Borshch and Valery I. Zhdanov
National Taras Shevchenko University of Kyiv, Ukraine

Received September 10, 2007, in final form November 28, 2007; Published online December 07, 2007

Abstract
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(ε). For linear EOS p = κε we obtain self-similar solutions in the case of plane, cylindrical and spherical symmetries. In the case of extremely stiff EOS (κ = 1) we obtain ''monopole + dipole'' and ''monopole + quadrupole'' axially symmetric solutions. We also found some nonlinear EOSs that admit analytic solutions.

Key words: relativistic hydrodynamics; exact solutions.

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