Universal algebraic relaxation of fronts propagating into an unstable state

Details Universal algebraic relaxation of fronts propagating into an unstable state Universal algebraic relaxation of fronts propagating into an unstable state

1997-07-16

arxiv.org/abs/patt-sol/9707004v1

Phys. Rev. Lett. 80, 1650 (1998) (revised version).

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, revtex, 3 figures

Scientific paper

10.1103/PhysRevLett.80.1650

We analyze ``pulled'' or ``linearly marginally stable'' fronts propagating into unstable states. While ``pushed'' fronts into meta- and unstable states relax exponentially, pulled fronts relax algebraically, and simultaneously the standard derivation of effective interface equations breaks down. We calculate all universal relaxation terms of uniformly translating pulled fronts. The leading $1/t$ and $1/t^{3/2}$ corrections to the velocity are determined by the dispersion relation of the linearized equation only. Our analysis sheds new light on the propagation mechanism of pulled fronts.

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