Periodically generated propagating pulses

TL;DR

This paper extends the asymptotic theory of the generalized Gunn effect to nonlinearities with a single stable zero, providing analytical wave solutions in a scalar model.

Contribution

It introduces a new theoretical extension for the Gunn effect in cases with one stable zero, with explicit analytical wave solutions.

Findings

Analytical construction of propagating pulses

Explicit asymptotic expressions derived

Extension of the generalized Gunn effect theory

Abstract

Certain equations with integral constraints have as solutions time-periodic pulses of a field-like unknown while a current-like unknown oscillates periodically with time. A general asymptotic theory of this phenomenon, the generalized Gunn effect, has been found recently. 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. 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.