According to the invention, the engine (I) includes a means for supplying fuel to the combustion chamber (7) of the fire tube (2), that comprises a variable-volume transfer chamber (9) for receiving fuel, a fuel transfer means (10) from the tank (4) of the engine (I) towards the transfer chamber (9), and injection means (11) for injecting fuel into the combustion chamber (7) from the transfer chamber (9). The engine further includes an elastic return means at least partially defined by the fuel contained in the transfer chamber (9).