Nonlinear waves in reaction-diffusion systems: The effect of transport memory

Motivated by the problem of determining stress distributions in granular ma terials, we study the effect of finite transport correlation times on the p ropagation of nonlinear wave fronts in reaction-diffusion systems. We obtai n results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-fro nt speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations an made possible by a pi ecewise linear representation of the nonlinearity.