  We present a model to describe an underdamped long Josephson junction coupled
to a singlemode electromagnetic cavity, and carry out numerical calculations
using this model in various regimes. The coupling may occur through either the
electric or the magnetic eld of the cavity mode. When a current is injected
into the junction, we nd that the time-averaged voltage exhibits self-induced
resonant steps due to coupling between the current in the junction and the
electric eld of the cavity mode. These steps are similar to those observed and
calculated in small Josephson junctions. When a soliton is present in the
junction (corresponding to a quantum of magnetic ux parallel to the junction
plates), the SIRS's disappear if the electric eld in the cavity is spatially
uniform. If the cavity mode has a spatially varying electric eld, there is a
strong coupling between the soliton and the cavity mode. This coupling causes
the soliton to become phase-locked to the cavity mode, and produces step-like
anomalies on the soliton branch of the IV characteristics. If the coupling is
strong enough, the frequency of the cavity mode is greatly red-shifted from its
uncoupled value. We present simple geometrical arguments which account for this
behavior.
