  In this paper, we describe analytically the propagation of Airy-type pulses
truncated by a finite-time aperture when second and third order dispersion
effects are considered. The mathematical method presented here, based on the
superposition of exponentially truncated Airy pulses, is very effective,
allowing us to avoid the use of time-consuming numerical simulations. We
analyze the behavior of the time truncated Ideal-Airy pulse and also the
interesting case of a time truncated Airy pulse with a "defect" in its initial
profile, which reveals the self-healing property of this kind of pulse
solution.
