X wave transformation under time discontinuity

We study the transformation of X waves under time discontinuities. We find out that the wave splits into two X waves, that the spatial features are conserved, and that the time features are altered, the wave being either compressed or expanded depending on the indices of refraction before and after the discontinuity. We also find that one of the transformed waves is time-reversed. We expect this work will provide solutions in applications such as plasma science and metamaterials.