  In this paper we set forth new exact analytical Superluminal localized
solutions to the wave equation for arbitrary frequencies and adjustable
bandwidth. The formulation presented here is rather simple, and its results can
be expressed in terms of the ordinary, so-called "X-shaped waves". Moeover, by
the present formalism we obtain the first analytical localized Superluminal
approximate solutions which represent beams propagating in dispersive media.
Our solutions may find application in different fields, like optics,
microwaves, radio waves, and so on. [PACS nos.: 03.50.De ; 41.20.Jb ; 83.50.Vr
; 62.30.+d ; 43.60.+d ; 91.30.Fn ; 04.30.Nk ; 42.25.Bs ; 46.40.Cd ; 52.35.Lv.
Keywords: Wave equation; Wave propagation; Optics; Localized beams;
Superluminal waves; Bessel beams; X-shaped waves; Acoustics; Mechanical waves;
Dispersion compensation; Seismology; Geophysics; Gravitational Waves;
Elementary particle physics].
