Numerical computation of an Evans function for travelling waves

K. Harley; P. v Heijster; R. Marangell; G. J. Pettet; M. Wechselberger

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arXiv · 1312.3685

Numerical computation of an Evans function for travelling waves

K. Harley·P. v Heijster·R. Marangell·G. J. Pettet·M. Wechselberger

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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 $c \geq 2 \sqrt{\delta}$ in the F-KPP equation.

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BibTeX RIS

K. Harley, P. v Heijster, R. Marangell, G. J. Pettet, M. Wechselberger. 2013-12-13. Numerical computation of an Evans function for travelling waves. https://arxiv.org/abs/1312.3685

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