Nonlinear transient waves in coupled phase oscillators with inertia

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.