Defects in Oscillatory Media: Toward a Classification
Defects in Oscillatory Media: Toward a Classification
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振荡介质的缺陷：分类
DOI：
10.1137/030600192
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发表时间：
2004
期刊：
影响因子：
--
通讯作者：
A. Scheel
中科院分区：
文献类型：
--
作者：
Bjorn Sandstede;A. Scheel
我们以系统的方式研究相干结构或缺陷，它们充当反应扩散系统中可能具有不同波数的波列之间的界面。我们提出将缺陷分为四种不同的缺陷类别，这些类别都已通过实验观察到。区分这些类别的特征是缺陷两侧的波列群速度的符号，相对于缺陷的速度进行测量。使用空间动力学描述，其中缺陷对应于不适定伪椭圆方程的同宿和异宿连接，然后我们将缺陷的鲁棒性特性与其光谱稳定性特性联系起来。最后，我们说明所有四种类型的缺陷都作为相滑涡的扰动出现在一维三次五次金兹堡-朗道方程中。
We investigate, in a systematic fashion, coherent structures, or defects, which serve as interfaces between wave trains with possibly different wavenumbers in reaction-diffusion systems. We propose a classification of defects into four different defect classes which have all been observed experimentally. The characteristic distinguishing these classes is the sign of the group velocities of the wave trains to either side of the defect, measured relative to the speed of the defect. Using a spatial-dynamics description in which defects correspond to homoclinic and heteroclinic connections of an ill-posed pseudoelliptic equation, we then relate robustness properties of defects to their spectral stability properties. Last, we illustrate that all four types of defects occur in the one-dimensional cubicquintic Ginzburg–Landau equation as a perturbation of the phase-slip vortex.