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