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arXiv · 1802.07676

Nonlinear stability of source defects in oscillatory media

Margaret Beck·Toan T. Nguyen·Björn Sandstede·Kevin Zumbrun
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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.

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Margaret Beck, Toan T. Nguyen, Björn Sandstede, Kevin Zumbrun. 2018-02-21. Nonlinear stability of source defects in oscillatory media. https://arxiv.org/abs/1802.07676

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