Nikolaevskiy equation with dispersion.
Nikolaevskiy equation with dispersion.
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具有色散的尼古拉耶夫斯基方程。
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
S. Cox
中科院分区：
文献类型：
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作者：
Eman Simbawa;P. Matthews;S. Cox
尼古拉耶夫斯基方程最初是作为地震波的模型提出的，也是包含中性“Goldstone”模式的各种系统的模型，包括电对流和反应扩散系统。众所周知，在图案形成的开始，至少当方程中的色散项被抑制时，至少当方程中的色散项被抑制时，表现出混沌动力学，这在以前的分析中是常见的。本文研究了恢复色散项的效果。结果表明，这些项可以稳定一些空间周期行波，这使得我们可以研究行波的失稳和向混沌的转变。行波的二次稳定性图(“巴斯气球”)可能非常复杂。
The Nikolaevskiy equation was originally proposed as a model for seismic waves and is also a model for a wide variety of systems incorporating a neutral "Goldstone" mode, including electroconvection and reaction-diffusion systems. It is known to exhibit chaotic dynamics at the onset of pattern formation, at least when the dispersive terms in the equation are suppressed, as is commonly the practice in previous analyses. In this paper, the effects of reinstating the dispersive terms are examined. It is shown that such terms can stabilize some of the spatially periodic traveling waves; this allows us to study the loss of stability and transition to chaos of the waves. The secondary stability diagram ("Busse balloon") for the traveling waves can be remarkably complicated.