Excitation of the Josephson plasma radiation by a fluxon moving in an annular Josephson junction is studied experimentally, numerically, and using an analytical approach. An externally applied magnetic field H forms a cosinelike potential relief for the fluxon in a ring-shaped junction. The motion of the fluxon in the junction leads to an emission of plasma waves, which give rise to a resonance at a certain fluxon velocity. The experimental data agree well with numerical simulations which indicate a locking of the fluxon to the radiation frequency. The peculiar feature indicated by both experiment and numerical simulations is the shape of the resonance in the current-voltage (I − V) characteristic which shows a clear backbending, with a negative differential resistance. The analytical approach developed in this work is based on the perturbation theory for radiation emission generated by a kink in the perturbed sine-Gordon equation. To explain the observed effect, we introduce an addition to the perturbation theory, which proves to be crucial for explanation of the backbending I − V curves: We take into account the fact that the background radiation field, supported by a balance between emission from the moving kink and dissipative absorption, narrows the junction’s plasma frequency gap. ... mehrIn the case when the emission has a resonant character, even a small change of the gap produces a strong reciprocal effect on the emission power. Following this idea, we develop a fully analytical self-consistent approximation that readily allows us to obtain the backbending I − V curves.