Periodic Recycling and Motion of Wavefronts in a Model of the Gunn Effect with Saturating Current Characteristics

Abstract

Certain equations with integral constraints have as solutions time-periodic recycling of pulses of a field-like unknown at boundaries while a current-like unknown oscillates periodically with time. A general asymptotic theory of this phenomenon, the generalized Gunn effect, has been recently found. Here we extend this theory to the case of nonlinearities having only one stable zero, which is the case for the usual Gunn effect in n-GaAs where the velocity-field characteristics has a local maximum after which the velocity decreases to a constant for large fields. The key of our theory is that we characterize the forefront and backfront of a given expanding or contracting pulse as certain trajectories in a phase plane and identify their velocities. Our ideas are presented in the context of a simple scalar model where the waves can be constructed analytically and explicit expressions for asymptotic approximations can be found.