  Like the inertia of a physical body describes its tendency to resist changes
of its state of motion, inertia of an oscillator describes its tendency to
resist changes of its frequency. Here we show that finite inertia of individual
oscillators enables nonlinear phase waves in spatially extended coupled
systems. Using a discrete model of coupled phase oscillators with inertia, we
investigate these wave phenomena numerically, complemented by a continuum
approximation that permits the analytical description of the key features of
wave propagation in the long-wavelength limit. The ability to exhibit traveling
waves is a generic feature of systems with finite inertia and is independent of
the details of the coupling function.
