  We study numerically and analytically the shape of a single fluxon moving in
a double stacked Josephson junctions (SJJ's) for various junction parameters.
We show that the fluxon in a double SJJ's consists of two components, which are
characterized by different Swihart velocities and Josephson penetration depths.
The weight coefficients of the two components depend on the parameters of the
junctions and the velocity of the fluxon. It is shown that the fluxon in SJJ's
may have an unusual shape with an inverted magnetic field in the second
junction when the velocity of the fluxon is approaching the lower Swihart
velocity. Finally, we study the influence of fluxon shape on flux-flow
current-voltage characteristics and analyze the spectrum of Cherenkov radiation
for fluxon velocity above the lower Swihart velocity. Analytic expression for
the wavelength of Cherenkov radiation is derived.
