Nonlinear stability of source defects in oscillatory media
Files
First author draft
Date
2018-02-21
DOI
Authors
Beck, Margaret
Nguyen, Toan
Sandstede, Bjorn
Zumbrun, Kevin
Version
OA Version
First author draft
Citation
Margaret Beck, Toan Nguyen, Bjorn Sandstede, Kevin Zumbrun. "Nonlinear stability of source defects in oscillatory media." Preprint, on arXiv https://arxiv.org/abs/1802.07676
Abstract
In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects are important as organizing centers of more complicated flows. Our analysis uses spatial dynamics combined with an instantaneous phase-tracking technique to obtain detailed pointwise estimates describing perturbations to lowest order as a phase-shift radiating outward at a linear rate plus a pair of localized approximately Gaussian excitations along the phase-shift boundaries; we show that in the wake of these outgoing waves the perturbed solution converges time-exponentially to a space-time translate of the original source pattern.