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

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.

References in corpus (9)

• Genealogies of rapidly adapting populations
• The traveling wave approach to asexual evolution: Muller's ratchet and speed of adaptation
• The noisy edge of traveling waves
• Effect of selection on ancestry: an exactly soluble case and its phenomenological generalization
• Exact solution and precise asymptotics of a Fisher-KPP type front
• Quantum chromodynamics at high energy and statistical physics
• Phenomenological picture of fluctuations in branching random walks
• An exactly solvable travelling wave equation in the Fisher-KPP class
• Vanishing corrections for the position in a linear model of FKPP fronts

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• Pushed, pulled and pushmi-pullyu fronts of the Burgers-FKPP equation
• Monte Carlo study of the tip region of branching random walks evolved to large times