  We investigate the existence and stability of travelling wave solutions in a
continuum field of non-locally coupled identical phase oscillators with
distance-dependent propagation delays. A comprehensive stability diagram in the
parametric space of the system is presented that shows a rich structure of
multi-stable regions and illuminates the relative influences of time delay, the
non-locality parameter and the intrinsic oscillator frequency on the dynamics
of these states. A decrease in the intrinsic oscillator frequency leads to a
break-up of the stability domains of the traveling waves into disconnected
regions in the parametric space. These regions exhibit a tongue structure for
high connectivity whereas they submerge into the stable region of the
synchronous state for low connectivity. A novel finding is the existence of
forbidden regions in the parametric space where no phase-locked solutions are
possible. We also discover a new class of non-stationary \textit{breather}
states for this model system that are characterized by periodic oscillations of
the complex order parameter.
