A theory of Josephson vortices-multikinks moving with a constant velocity i
s formulated for nondissipative Josephson junctions on the basis of the Aub
ry-Volkov analytical model. Cherenkov trapping of Swihart waves by moving v
ortices is predicted. A description of the structure of vortices which is d
ue to the waves trapped by them is given. It is predicted that the characte
ristic velocities of the moving vortices are discrete. This phenomenon is d
ue to the structure of the Swihart waves trapped by the vortices. The conce
pt of gluing of elementary Josephson vortices by Swihart waves in a coheren
tly-phased, multivortex, structure is advanced. (C) 2000 MAIK "Nauka/Interp
eriodica".