The motion of a shock wave through a non-uniform one-dimensional medium   in the case of arbitrary equation of state
  The derivation of the equation of one-dimensional movement of a solitary shock wave is given. This derivation shows, that the differential equation of movement of a solitary plane shock wave in the channel with variable area, is exact, if simplifying assumptions, made during derivation, are realized. But these assumptions in plane geometry it is possible to realize only approximately; situation with spherical and cylindrical shock waves is opposite. 
Serge A. Serov