At present, virtually all jet engines are based on the Brighton thermodynamic cycle (combustion at constant pressure). The improvement of such engines has already reached its technological limit. A significant increase in the efficiency of jet engines (by 20%-25%) can be provided by a transition to the Fickett-Jacobs[4] thermodynamic cycle which uses detonation combustion. One possible realization is a rotating detonation engine (RDE) in which the combustion chamber is the space between two coaxial cylinders. In an ideal scheme, a fuel mixture is supplied from one end which is ignited by a shock wave rotating in the annular gap with the Chapman-Jouguet velocity, i.e., with a speed equal to the speed of sound relative to the combustion products. It is known that in reality, a much more complex system of gas dynamic discontinuities is formed, consisting of triple configurations of shock waves. Detonation occurs only on the so-called Mach stems and not throughout the entire volume. In this paper, the possibility of creating a traveling overdriven wave by moving an obstacle behind the detonation area is investigated. Particular attention is paid to the initial stage - detonation initiation. A numerical method of the second order of accuracy with a finite rate of chemical reactions is used.