Exact solution and precise asymptotics of a Fisher–KPP type front

The present work concerns a version of the Fisher–KPP equation where the nonlinear term is replaced by a saturation mechanism, yielding a free boundary problem with mixed conditions. Following an idea proposed in Brunet and Derrida (2015 J. Stat. Phys . 161 801), we show that the Laplace transform of the initial condition is directly related to some functional of the front position μ t . We then obtain precise asymptotics of the front position by means of singularity analysis. In particular, we recover the so-called Ebert and van Saarloos correction (Ebert and van Saarloos 2000 Physica D 146 1), we obtain an additional term of order log ⁡ t / t in this expansion, and we give precise conditions on the initial condition for those terms to be present.