On the propagation of sonic discontinuities in the unsteady flow of a perfect gas

The magnitude of discontinuities of the first derivatives of flow quantities in the unsteady flow of a perfect gas are shown to satisfy Riccatti equations along the orthogonal trajectories of sonic singular surfaces. These equations are greatly simplified if they are transformed to equations along the bicharacteristic curves in the characteristic manifold defined by the union of all of these sonic singular surfaces. When this is done an explicit criterion for the decay or 'blow up' of sonic discontinuities can be given.