The effect of the induced Compton and Raman scattering on short, bright radio pulses is investigated. It is shown that when a single pulse propagates through the scattering medium, the effective optical depth is determined by the duration of the pulse but not by the scale of the medium. The induced scattering could hinder propagation of the radio pulse only if close enough to the source a dense enough plasma is present. The induced scattering within the rel-ativistically moving source places lower limits on the Lorentz factor of the source. The results are applied to the recently discovered short extragalactic radio pulse.
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