107 citations · 1.1k across the 120 of their papers we have counts for
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Nonlocalized modulation of periodic reaction diffusion waves: Nonlinear stability
Mathew Johnson, Pascal Noble, L. Miguel Rodrigues +1
By a refinement of the technique used by Johnson and Zumbrun to show stability under localized perturbations, we show that spectral stability implies nonlinear modulational stabili…
Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation
Mathew Johnson, Pascal Noble, L. Miguel Rodrigues +1
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems…
Toward nonlinear stability of sources via a modified Burgers equation
Margaret Beck, Toan Nguyen, Bjorn Sandstede +1
Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at to spatially periodi…