GE is bench testing the concept, which basically involves using a pulse detonation engine (PDE) in place of the high pressure turbine.

Basically, a PDE is a pulse jet, like that of the V-1 “Buzz Bomb”, but instead of igniting the fuel normally, where the flame front front progresses at subsonic speeds, it detonates the fuel (the flame front moves at supersonic speeds).

What I’ve read mostly is its potential to replace high speed turbojets, but this shows that it could be applied to civil high bypass engines by replacing the HP compressor and turbine.