Periodic generation and propagation of traveling fronts in dc voltage   biased semiconductor superlattices
  The continuum limit of a recently-proposed model for charge transport in resonant-tunneling semiconductor superlattices is analyzed. It is described by a nonlinear hyperbolic integrodifferential equation on a one-dimensional spatial support, supplemented by shock and entropy conditions. For appropriate parameter values, a time-periodic solution is found in numerical simulations of the model. An asymptotic theory shows that the time-periodic solution is due to recycling and motion of shock waves representing domain walls connecting regions of the superlattice where the electric field is almost uniform. 
Luis L. Bonilla, Manuel Kindelan, Miguel Moscoso, Stephanos Venakides