Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff

Details Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff Validity of the Brunet-Derrida formula for the speed of pulled fronts with a cutoff

2007-06-25

arxiv.org/abs/0706.3671v1

European Physical Journal B 61 (2008) 331

Nonlinear Sciences

Pattern Formation and Solitons

8 pages, 3 figures

Scientific paper

10.1140/epjb/e2008-00069-1

We establish rigorous upper and lower bounds for the speed of pulled fronts with a cutoff. We show that the Brunet-Derrida formula corresponds to the leading order expansion in the cut-off parameter of both the upper and lower bounds. For sufficiently large cut-off parameter the Brunet-Derrida formula lies outside the allowed band determined from the bounds. If nonlinearities are neglected the upper and lower bounds coincide and are the exact linear speed for all values of the cut-off parameter.

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