Relativistic centered wave of compression

The problem relativistic isentropic compression by a plain piston of substance with a power equation of state is reduced to self-similar state and it is solved. Thereby the relativistic centered wave of compression is constructed. The numerical and approximate solutions in ultrarelativistic and nonrelativistic limits are received. The features, which carry the relativistic dynamics at transition to limiting compression, are considered. The evolutions of space and time dependences on the piston are described. The estimations of time of transition are resulted in relativistic limit in cylindrical and spherical geometry.