A note of the convergence of the Fisher-KPP front centred around its $\alpha$-level

Julien Berestycki, Éric Brunet

We consider the solution $u(x,t)$ of the Fisher-KPP equation ${\partial }_{t}u={\partial }_x^{2}u+u-u^2$ centred around its $\alpha$-level ${\mu }_t^{(\alpha )}$ defined as $u({\mu }_t^{(\alpha )},t)=\alpha$. It is well k…