2018/02/21 by Margaret Beck, Beck, Margaret, Toan T. Nguyen +5
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Stability and Controllability of Differential Equations #math.AP #math.DS
paper · pdf · doi:10.48550/arxiv.1802.07676
43 pages, 5 figures
arxiv created 2018/02/21 · openalex publication_date 2018/02/21 · arxiv updated 2018/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.