Airy Pulse Transformation by an Accelerated Medium Boundary

In the statement of a problem with a moving boundary there is one more idealization, namely, movement stationarity assuming that the movement has begun at infinite past time. Abandoning this idealization, by considering a movement that begins at a finite moment of time, leads to the appearance of new peculiarities in the wave transformation on a moving boundary. In this paper such peculiarities are considered with an abrupt uniform movement of a boundary beginning at zero moment of time, as well as with a smooth "turning on" of a boundary movement according to a relativistic uniformly accelerated law. In the latter approach the continuity of a boundary velocity change allows the development of the evolution of the wave transformation process to be traced.