An engine contains a compressor stage, a compressor plenum, an inlet valving stage, a PDC stage, a PDC exit nozzle stage, a transition stage, a high pressure turbine stage, a turbine plenum, and a low pressure turbine stage. The PDC stage contains at least one pulse detonation combustor and each of the compressor plenum, PDC exit nozzle stage and turbine plenum contain a volume used to reduce and / or widen pressure peaks generated by the operation of the PDC stage.