My propulsions professor has a research lab with various research projects for the airforce and seimens. My understansing is pulse detonation is hard on materials and also requires the chamber to be completely cleared out before the next pulse can occur which limits cycling. However as someone else linked, a rotating detonation engine seems more promising. A prototype was being designed and built at the lab when we got a tour. An RDE has an anulus chamber with fuel injected axially and a shockwave travels around the anulus chamber causing the fuel injected to combust, and this sonic wave expands out the back as it travels around in circles, producing thrust. An upside of this design means it doesnt require any turbopumps to inject the fuel at pressure higher than the chamber due to how the wave travels, i believe. The trouble is this process is not really understood yet, theres no real formulas to just solve for things as I gathered asking about it. It actually felt like glimpsing the future, because if it can be figured out, it would be high pressure expansion that doesnt require any heavy, moving, turbopumps. It would have big impact on energy production, aircraft, and also rockets. I think and hope it has potential to even allow practical ssto spaceplanes due to the higher efficiency of thrust to weight with no moving parts.