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



C E. Elmer, E S. Vanleck


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.
Siam Journal on Applied Mathematics
No. 5


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


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)


If you have any questions about this publication or are having problems accessing it, please contact

Created March 1, 2001, Updated June 2, 2021