Stability of slowly varying traveling waves in Josephson arrays

We study the stability of slowly varying (in frequency and horizontal phase shift delta) traveling waves in two-dimensional Josephson arrays with f magnetic flux quanta per plaquette at high Josephson frequencies. The dynamics of long-wavelength phase modulations is shown to be governed by a Burger's-like equation, which allows the formation of shocks (or fronts) separating regions with different frequency and phase shift. The front velocity is given by the ratio of the difference in frequencies over the difference in phase shifts across it. We find that there is a band of diffusively stable states for delta is an element of[2 pi f,pi]. These results are in good agreement with the numerical computations.