Published in

Springer Verlag, Journal of Statistical Physics, 4(161), p. 801-820

DOI: 10.1007/s10955-015-1350-6

Links

Tools

Export citation

Search in Google Scholar

An Exactly Solvable Travelling Wave Equation in the Fisher–KPP Class

Journal article published in 2015 by Eric Brunet, Éric Brunet, Bernard Derrida
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Green circle
Preprint: archiving allowed
Green circle
Postprint: archiving allowed
Red circle
Published version: archiving forbidden
Data provided by SHERPA/RoMEO

Abstract

For a simple one dimensional lattice version of a travelling wave equation, we obtain an exact relation between the initial condition and the position of the front at any later time. This exact relation takes the form of an inverse problem: given the times $t_n$ at which the travelling wave reaches the positions $n$, one can deduce the initial profile. We show, by means of complex analysis, that a number of known properties of travelling wave equations in the Fisher-KPP class can be recovered, in particular Bramson's shifts of the positions. We also recover and generalize Ebert-van Saarloos' corrections depending on the initial condition.