Wavenumber selection in coupled transport equations
Arnd Scheel and Angela Stevens
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Submission date: 20. Sep. 2016
published in: Journal of mathematical biology, 75 (2017) 5, p. 1047-1073
DOI number (of the published article): 10.1007/s00285-017-1107-8
Keywords and phrases: traveling wave, standing wave, balance laws, coupled transport equations, invasion fronts, wavenumber selection
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We study mechanisms for wavenumber selection in a minimal model for run-and-tumble dynamics. We show that nonlinearity in tumbling rates induces the existence of a plethora of traveling- and standing-wave patterns, as well as a subtle selection mechanism for the wavenumbers of spatio-temporally periodic waves. We comment on possible implications for rippling patterns observed in colonies of myxobacteria.