Detonation engines are not just for rockets, but a wide variety of applications. They are in theory more efficient that what we have today, but also very complicated to model, because fluid dynamics are really complicated.
The important bit about detonation engines is that detonation in the context means a shock wave that expands faster than the speed of sound in the medium. If it goes slower you have a deflagration not a detonation. (They look more or less the same to a layperson looking at something going boom.)
Stuff like pulse detonation engines have been build and tested and rotation detonation engines are a thing people at places like NASA hope to build.
The result would be more efficient rockets and jet-engine with fewer moving parts.
It is not easy though. The math is hard and the margin of error for things that explode is low.
Still it is a nice idea if it can be made to work.
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