The effect of spatial modulations on codimension-2 bifurcations

W. Zimmermann; Hans Armbruster; L. Kramer; W. Kuang

doi:10.1209/0295-5075/6/6/006

The effect of spatial modulations on codimension-2 bifurcations

W. Zimmermann, Hans Armbruster, L. Kramer, W. Kuang

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

The stability of stationary patterns and travelling waves against arbitrary fluctuations in spatially extended systems are investigated for the first time near the codimension-2 point. An important result is that travelling waves (and also standing waves) lose stability in some range via Benjamin-Feir resonance if the stationary pattern bifurcates inversely, in qualitative agreement with measurements on binary fluid mixtures. The results presented could stimulate further investigations.

Original language	English (US)
Pages (from-to)	505-510
Number of pages	6
Journal	EPL
Volume	6
Issue number	6
DOIs	https://doi.org/10.1209/0295-5075/6/6/006
State	Published - Jul 15 1988
Externally published	Yes

ASJC Scopus subject areas

General Physics and Astronomy

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10.1209/0295-5075/6/6/006

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title = "The effect of spatial modulations on codimension-2 bifurcations",

abstract = "The stability of stationary patterns and travelling waves against arbitrary fluctuations in spatially extended systems are investigated for the first time near the codimension-2 point. An important result is that travelling waves (and also standing waves) lose stability in some range via Benjamin-Feir resonance if the stationary pattern bifurcates inversely, in qualitative agreement with measurements on binary fluid mixtures. The results presented could stimulate further investigations.",

author = "W. Zimmermann and Hans Armbruster and L. Kramer and W. Kuang",

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AU - Kuang, W.

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Y1 - 1988/7/15

N2 - The stability of stationary patterns and travelling waves against arbitrary fluctuations in spatially extended systems are investigated for the first time near the codimension-2 point. An important result is that travelling waves (and also standing waves) lose stability in some range via Benjamin-Feir resonance if the stationary pattern bifurcates inversely, in qualitative agreement with measurements on binary fluid mixtures. The results presented could stimulate further investigations.

AB - The stability of stationary patterns and travelling waves against arbitrary fluctuations in spatially extended systems are investigated for the first time near the codimension-2 point. An important result is that travelling waves (and also standing waves) lose stability in some range via Benjamin-Feir resonance if the stationary pattern bifurcates inversely, in qualitative agreement with measurements on binary fluid mixtures. The results presented could stimulate further investigations.

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The effect of spatial modulations on codimension-2 bifurcations

Abstract

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