  We present a systematic study of the Cherenkov radiation of Josephson plasma
waves by fast moving fluxon in a stack of coupled long Josephson junctions for
different fluxon modes. It is found that at some values of parameters
current-voltage characteristic may exhibit a region of the back-bending on the
fluxon 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 emerge on the
top of the fluxon step. We present more exact formulas which describe the
position of such resonances taking into account difference between junction and
non-linear corrections. The possibility of direct detection of the Cherenkov
radiation in junctions of linear geometry is discussed.
