Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Traveling Wave Solutions for Bistable Differential-Difference Equations With Periodic Diffusion

Published

Author(s)

C E. Elmer, E S. Vanleck

Abstract

We consider traveling wave solutions to spatially discrete reaction-diffusion equations with nonlocal variable diffusion and bistable nonlinearities. For the case of spatially periodic diffusion we obtain analytic solutions for the traveling wave problem using a piecewise linear nonlinearity. The formula for the wave forms is implicitly defined in the general periodic case and we provide an explicit formula for the case of period two diffusion. We present numerical results for the cases of homogeneous, period two, and period four diffusion coefficients using a cubic nonlinearity, and uncover, numerically, a period doubling bifurcation in the wave speed versus detuning parameter relation.
Citation
Siam Journal on Applied Mathematics
Volume
61
Issue
No. 5

Keywords

differential-difference equation, lattice differential equation, periodic diffusion, traveling wave solution

Citation

Elmer, C. and Vanleck, E. (2001), Traveling Wave Solutions for Bistable Differential-Difference Equations With Periodic Diffusion, Siam Journal on Applied Mathematics (Accessed June 16, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created March 1, 2001, Updated June 2, 2021