Memory effect, conformal symmetry and gravitational plane waves

We discuss in some detail the interaction of classical particles, including the scattering and memory effect, with a pulse of gravitational plane wave. The key point is the conformal symmetry of gravitational plane waves. In particular, we obtain, in the limit of short pulse, some results for impulsive gravitational waves. Furthermore, in the general case, we give certain conditions which allow us to completely describe the interaction in terms of the singular Baldwin-Jeffery-Rosen coordinates.