  We report experimental and numerical study of microwave-induced flow of
vortices in long Josephson junctions at zero dc magnetic field. Our intriguing
observation is that applying an ac-bias of a small frequency $f \ll f_p $ and
sufficiently large amplitude changes the current-voltage characteristics
($I$-$V$ curve) of the junction in a way similar to the effect of dc magnetic
field, well known as the flux-flow behavior. The characteristic voltage $V$ of
this low voltage branch increases with the power $P$ of microwave radiation as
$V_{s}\propto P^{\alpha}$ with the index $\alpha \simeq 0.5 $. Experiments
using a low-temperature laser scanning microscope unambiguously indicate the
motion of Josephson vortices driven by microwaves. Numerical simulations agree
with the experimental data and show strongly {\it irregular} vortex motion. We
explain our results by exploiting an analogy between the microwave-induced
vortex flow in long Josephson junctions and incoherent multi-photon absorption
in small Josephson junctions in the presence of large thermal fluctuations. In
the case of long Josephson junctions the spatially-temporal chaos in the vortex
motion mimics the thermal fluctuations. In accordance with this analogy, a
control of the intensity of chaos in a long junction by changing its damping
constant leads to a pronounced change in the shape of the $I$-$V$ curve. Our
results provide a possible explanation to previously measured but not yet
understood microwave-driven properties of intrinsic Josephson junctions in
high-temperature superconductors.
