title: Numerical computation of an Evans function for travelling waves.
abstract: We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller-Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed c≥2√δ in the F-KPP equation.
authors.affiliation: Mathematical Sciences School, Queensland University of Technology, Brisbane, QLD 4000 Australia.
authors.forename: K
authors.initials: K
authors.lastname: Harley
authors.affiliation: Mathematical Sciences School, Queensland University of Technology, Brisbane, QLD 4000 Australia.
authors.forename: P
authors.initials: P
authors.lastname: van Heijster
authors.affiliation: School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006 Australia. Electronic address: robert.marangell@sydney.edu.au.
authors.forename: R
authors.initials: R
authors.lastname: Marangell
authors.affiliation: Mathematical Sciences School, Queensland University of Technology, Brisbane, QLD 4000 Australia.
authors.forename: G J
authors.initials: GJ
authors.lastname: Pettet
authors.affiliation: School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006 Australia.
authors.forename: M
authors.initials: M
authors.lastname: Wechselberger
mesh_terms: D018407:Bacterial Physiological Phenomena; D002633:Chemotaxis; D008954:Models, Biological
keywords: Evans functions; Fisher-KPP equation; Keller-Segel equations; Spectral stability; Travelling waves