I just checked and indeed there is research.

The most popular model that we all know is called the Gartner Hype Cycle. https://www.gartner.com/en/research/methodologies/gartner-hy...

Arxiv has a few articles on hype cycles for example:

"A simple interpretation of the growth of scientific/technological research impact leading to hype-type evolution curves", Campani, 2014. https://arxiv.org/abs/1410.8685

"Hype Cycle Dynamics: Microscopic Modeling and Detection", Hashemi, 2018. https://arxiv.org/abs/1809.08939

You can also type "gartner hype cycle" in Scholar or sci-hub and there are many hits.

Not that I'm aware of. It's more a comment on how at some point the press overhypes some tech which then leads to an inevitable correction. Hopefully it's true value is appreciated afterwards but that's not a given.