Cherenkov radiation from fluxon in a stack of coupled long Josephson junctions

We present a systematic study of the Cherenkov radiation of Josephson plasm a waves by fast moving fluxon in a stack of coupled long Josephson junction s for fluxon modes. It is found that at some values of parameters current-v oltage characteristic may exhibit a region of the back-bending on the fluxo n step. In the opposite limit the emission of the Cherenkov radiation takes place. In the annular junctions of moderate length the interaction of the emitted waves with fluxon results in the novel resonances which describe th e position of such resonances taking into account difference between juncti on and non-linear corrections. The possibility of direct detection of the C herenkov radiation in junctions of linear geometry is discussed.