  In this paper we use a unidirectional decomposition capable of furnishing
localized wave pulses, with luminal and superluminal peak velocities, in exact
form and totally free of backward components, which have been a chronic problem
for such wave solutions. This decomposition is powerful enough for yielding not
only ideal nondiffracting pulses but also their finite energy versions still in
exact analytical closed form. Another advantage of the present approach is
that, since the backward spectral components are absent, the frequency spectra
of the pulses do not need to possess ultra-widebands, as it is required by the
usual localized waves (LWs) solutions obtained by other methods. Finally, the
present results bring the LW theory nearer to the real experimental
possibilities of usual laboratories.
