Effects of transport memory in wave fronts in a bistable reaction–diffusion system

Abstract

In this paper, we analyze transport memory effects in bistable reaction−diffusion systems. Traveling wave fronts are obtained for two interesting cases: (i)The nonlinear reaction term is treated without any approximation by factorization method. We find that transport memory effects appear to play a key role as it prevents the concentration or the amplitude from taking negative values. These memory effects enter the dynamics of the reaction diffusion systems through their influence on the speed of the traveling wave fronts. (ii) The nonlinear reaction term is replaced by a piecewise linear approximate form. We obtain a system of differential equations describing the three damped harmonic oscillators, one of which has a negative mass and the others positive masses.