Periodically Generated Propagating Pulses

  title={Periodically Generated Propagating Pulses},
  author={L. Bonilla and M. Kindelan and J. Keller},
  journal={SIAM J. Appl. Math.},
Certain equations with integral constraints have as solutions time-periodic pulses of a fieldlike unknown while a currentlike 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… Expand
3 Citations
Non-linear dynamics of semiconductor superlattices
In the last decade, non-linear dynamical transport in semiconductor superlattices (SLs) has witnessed significant progress in theoretical descriptions as well as in experimentally observed non-linearExpand
Workshop: Material Theories Table of Contents
. . . Mathematics Subject Classification (2000): AMS-CLASSIFICATION. Introduction by the Organisers Physical Sciences and, in particular, Mechanics, have always played an important role as a sourceExpand


Solitary waves in semiconductors with finite geometry and the Gunn effect
An asymptotic analysis of the Gunn effect (oscillations of the current through a semiconductor under constant voltage bias) is given. The electric field inside the one-dimensional semiconductor isExpand
Universality of the Gunn effect: Self-sustained oscillations mediated by solitary waves
The Gunn effect consists of time-periodic oscillations of the current flowing through an external purely resistive circuit mediated by solitary wave dynamics of the electric field on an attachedExpand
Traveling wave solutions of a nerve conduction equation.
The slower pulse is shown to be unstable and the faster one to be stable, confirming conjectures which have been made before for other nerve conduction equations, and the stability of the solutions is analyzed. Expand
The Gunn Effect: Instability of the Steady State and Stability of the Solitary Wave in Long Extrinsic Semiconductors
The linear stability of the solitary wave characteristic of the Gunn effect is proved for an idealized electron velocity curve in the zero diffusion limit. Expand
Slowly Modulated Two-Pulse Solutions in the Gray--Scott Model I: Asymptotic Construction and Stability
An existence study for solutions consisting of two symmetric pulses moving apart from each other with slowly varying velocities corresponding to a "mildly strong" pulse interaction problem in which the inhibitor concentration varies on long spatial length scales. Expand
Asymptotic analysis of the Gunn effect with realistic boundary conditions
A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundaryExpand
TOPICAL REVIEW: Theory of nonlinear charge transport, wave propagation, and self-oscillations in semiconductor superlattices
Nonlinear charge transport in semiconductor superlattices under strong electric fields parallel to the growth direction results in rich dynamical behaviour including the formation of electric fieldExpand
A simple analysis of stable domain propagation in the Gunn effect
An analytical treatment of uniformly propagating stable domains is developed for the case when the electrons have a field-independent diffusion coefficient and follow an arbitrary staticExpand
Travelling pulses in reaction-diffusion systems under global constraints
Abstract:The influence of global inhibition on travelling pulses both in infinite and in finite periodic systems is investigated. Analytic investigation of the modified piecewise linearExpand
Gunn instability in finite samples of GaAs. II: Oscillatory states in long samples
Abstract An asymptotic description is given of the well known phenomenon of charge density waves propagating in long samples of n-type GaAs with Ohmic contacts and voltage bias. Depending on theExpand