Speed Selection Mechanism for Propagating Fronts in Reaction-Diffusion Systems with Multiple Fields

Abstract

We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals in the comoving frames of reference. The unique velocity for which the center of a monotonic solution for a particular field is insensitive to the location of the ends of the finite interval is the velocity that is physically selected for that field, making thus the solution approximately translation invariant. The fronts for the various fields may propagate at different speeds, all of them being determined through this mechanism. We present analytic results for the case of piecewise parabolic potentials, and numerical results for other cases.Comment: TeX file, 18 pages and 5 postscript figures, to appear in Physical Review