  The flux-flow dynamics in a long Josephson junction is studied both
analytically and numerically. A realistic model of the junction is considered
by taking into account a nonuniform current distribution, surface losses and
self-pumping effects. An approximate analytical solution of the modified
sine-Gordon equation is derived in the form of a unidirectional dense fluxon
train accompanied by two oppositely directed plasma waves. Next, some
macroscopic time-averaged quantities are calculated making possible to evaluate
the current-voltage characteristic of the junction. The results obtained by the
present method are compared with direct numerical simulations both for the
current-voltage characteristics and for the loss factor modulated spatially due
to the self-pumping. The comparison shows very good agreement for typical
junction parameters but indicates also some limitations of the method.
