Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation

Details Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation Nonlocalized modulation of periodic reaction diffusion waves: The Whitham equation

2011-05-25

arxiv.org/abs/1105.5044v2

Mathematics

Analysis of PDEs

Scientific paper

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 under small perturbations consisting of a nonlocalized modulation plus a localized perturbation. Here, we determine time-asymptotic behavior under such perturbations, showing that solutions consist to leading order of a modulation whose parameter evolution is governed by an associated Whitham averaged equation.

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