Dual Fronts Propagating into an Unstable State

The interface between an unstable state and a stable state usually develops a single confined front travelling with constant velocity into the unstable state. Recently, the splitting of such an interface into {\em two} fronts propagating with {\em different} velocities was observed numerically in a magnetic system. The intermediate state is unstable and grows linearly in time. We first establish rigorously the existence of this phenomenon, called ``dual front,'' for a class of structurally unstable one-component models. Then we use this insight to explain dual fronts for a generic two-component reaction-diffusion system, and for the magnetic system.Comment: 19 pages, Postscript, A

Dual Fronts Propagating into an Unstable State

. The interface between an unstable state and a stable state usually develops a single confined front travelling with constant velocity into the unstable state. Recently, the splitting of such an interface into two fronts propagating with different velocities was observed numerically in a magnetic system. The intermediate state is unstable and grows linearly in time. We first establish rigorously the existence of this phenomenon, called "dual front," for a class of structurally unstable one-component models. Then we use this insight to explain dual fronts for a generic two-component reaction-diffusion system, and for the magnetic system. - 2 - 1. Introduction Parabolic differential equations, such as the (complex) Ginzburg-Landau equation [CE, CH], occur in many domains of physics. We are here interested in this equation when considered on an infinite domain. Then, a well-known phenomenon is the formation of fronts (travelling waves), which are solutions whose shape is fixed in a f..