  In this paper we extend for the case of Maxwell equations the "X-shaped"
solutions previously found in the case of scalar (e.g., acoustic) wave
equations. Such solutions are localized in theory, i.e., diffraction-free and
particle-like (wavelets), in that they maintain their shape as they propagate.
In the electromagnetic case they are particularly interesting, since they are
expected to be Superluminal. We address also the problem of their practical,
approximate production by finite (dynamic) radiators. Finally, we discuss the
appearance of the X-shaped solutions from the purely geometric point of view of
the Special Relativity theory.
  [PACS nos.: 03.50.De; 1.20.Jb; 03.30.+p; 03.40.Kf; 14.80.-j.
  Keywords: X-shaped waves; localized solutions to Maxwell equations;
Superluminal waves; Bessel beams; Limited-dispersion beams; electromagnetic
wavelets; Special Relativity; Extended Relativity].
