U. Ebert et W. Van Saarloos, Breakdown of the standard perturbation theory and moving boundary approximation for "pulled" fronts, PHYS REPORT, 337(1-2), 2000, pp. 139-156
A moving boundary approximation or similar perturbative schemes for the res
ponse of a coherent structure like a front, vortex or pulse to external for
ces and noise can generally be derived if two conditions are obeyed: (i) th
ere must be a separation of the time scales of the dynamics on the inner an
d outer scale, and (ii) solvability-type integrals must converge. We point
out that both of these conditions are not satisfied for pulled fronts propa
gating into an unstable state: their relaxation on the inner scale is algeb
raic rather than exponential, and in conjunction with this, solvability int
egrals diverge. This behavior can be explained by the fact that the importa
nt dynamics of pulled fronts occurs in the leading edge of the front rather
than in the nonlinear internal front region itself. As a consequence, the
dynamical behavior of pulled fronts is often qualitatively different from t
he standard case in which fronts between two (meta)stable states are consid
ered, as has recently been established for the relaxation, the stochastic b
ehavior and the response to multiplicative noise. We here show that this is
also true for the coupling of pulled fronts to other fields. (C) 2000 Else
vier Science B.V. All rights reserved.