期刊
CONTEMPORARY PHYSICS
卷 53, 期 2, 页码 79-95出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/00107514.2011.642554
关键词
nonlinear physics; spatially extended systems; oscillations; turbulence; resonant forcing; spatial coupling
资金
- cluster of excellence Nanosystems Initiative Munich (NIM)
- Technische Universitat Munchen - Institute for Advanced Study
- German Excellence Initiative
The complex Ginzburg-Landau equation (CGLE), probably the most celebrated nonlinear equation in physics, describes generically the dynamics of oscillating, spatially extended systems close to the onset of oscillations. Using symmetry arguments, this article gives an easy access to this equation and an introduction into the rich spatiotemporal behaviour it describes. Starting out from the familiar linear oscillator, we first show how the generic model for an individual nonlinear oscillator, the so-called Stuart-Landau equation, can be derived from symmetry arguments. Then, we extend our symmetry considerations to spatially extended systems, arriving at the CGLE. A comparison of diffusively coupled linear and nonlinear oscillators makes apparent the source of instability in the latter systems. A concise survey of the most typical patterns in 1D and 2D is given. Finally, more recent extensions of the CGLE are discussed that comprise external, time-periodic forcing as well as nonlocal and global spatial coupling.
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