
SIGMA 3 (2007), 116, 11 pages arXiv:0709.1053
https://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
nonstationary inhomogeneous flows of the perfect fluid
with oneparametric equation of state (EOS) p = p(ε).
For linear EOS p = κε we obtain selfsimilar
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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