TY - JOUR
T1 - Pattern forming pulled fronts: Bounds and universal convergence
AU - Ebert, U.
AU - Spruijt, W.
AU - Saarloos, van, W.
PY - 2004
Y1 - 2004
N2 - We analyze the dynamics of pattern forming fronts which propagate into an unstable state, and whose dynamics is of the pulled type, so that their asymptotic speed is equal to the linear spreading speed v*. We discuss a method that allows to derive bounds on the front velocity, and which, hence, can be used to prove for, among others, the Swift–Hohenberg equation, the extended Fisher–Kolmogorov equation and the cubic complex Ginzburg–Landau equation, that the dynamically relevant fronts are of the pulled type. In addition, we generalize the derivation of the universal power law convergence of the dynamics of uniformly translating pulled fronts to both coherent and incoherent pattern forming fronts. The analysis is based on a matching analysis of the dynamics in the leading edge of the front, to the behavior imposed by the nonlinear region behind it. Numerical simulations of fronts in the Swift–Hohenberg equation are in full accord with our analytical predictions.
AB - We analyze the dynamics of pattern forming fronts which propagate into an unstable state, and whose dynamics is of the pulled type, so that their asymptotic speed is equal to the linear spreading speed v*. We discuss a method that allows to derive bounds on the front velocity, and which, hence, can be used to prove for, among others, the Swift–Hohenberg equation, the extended Fisher–Kolmogorov equation and the cubic complex Ginzburg–Landau equation, that the dynamically relevant fronts are of the pulled type. In addition, we generalize the derivation of the universal power law convergence of the dynamics of uniformly translating pulled fronts to both coherent and incoherent pattern forming fronts. The analysis is based on a matching analysis of the dynamics in the leading edge of the front, to the behavior imposed by the nonlinear region behind it. Numerical simulations of fronts in the Swift–Hohenberg equation are in full accord with our analytical predictions.
U2 - 10.1016/j.physd.2004.08.001
DO - 10.1016/j.physd.2004.08.001
M3 - Article
SN - 0167-2789
VL - 199
SP - 13
EP - 32
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-2
ER -