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> "Optical, radio, and X-ray follow-up has been made for most of the reported bursts, with no associated transients found."

What is a "transient" in this context?

I think they're looking for changes in the sky from those locations. Supernovae for example leave visible traces--clouds, rings, shock fronts, etc and emit all kinds of radio and x-rays. But FRB's not so much, it would seem, so far anyway.
I think this refers to a quick search through observations from other telescopes observing other EM frequency ranges ... to see if they saw short energy bursts at the same times. That's becoming common for, e.g., LIGO gravity wave observations.
Forgive my ignorance, can someone please explain what this potentially means?
The three bursts 1ms apart don't appear to be natural (or at least, we don't currently understand how they may occur naturally). The signal may be extraterrestrial.
If it is from a three-stage nuke it might be terrestrial. IIRC nukes have a characteristic double-pulse 1ms apart.