A new approach to computing the asymptotics of the position of Fisher-KPP fronts

TL;DR

This paper introduces a novel method for calculating the asymptotic position of Fisher-KPP fronts using Laplace transforms and singularity analysis, providing precise asymptotics and demonstrating robustness for generalization.

Contribution

It presents a new approach based on an exact relation between Laplace transforms and front positions, advancing the analytical tools for Fisher-KPP equations.

Findings

Accurately computes front position asymptotics up to O(log t / t)

Method is robust and adaptable to other front equations

Provides a new analytical framework for Fisher-KPP front analysis

Abstract

This paper presents a novel way of computing front positions in Fisher-KPP equations. Our method is based on an exact relation between the Laplace transform of the initial condition and some integral functional of the front position. Using singularity analysis, one can obtain the asymptotics of the front position up to the O(log t/t) term. Our approach is robust and can be generalised to other front equations.