The world of the complex Ginzburg-Landau equation
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The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community. It describes a vast variety of phenomena from nonlinear waves to second-order phase transitions, from superconductivity, superfluidity, and Bose-Einstein condensation to liquid crystals and strings in field theory. The authors give an overview of various phenomena described by the complex Ginzburg-Landau equation in one, two, and three dimensions from the point of view of condensed-matter physicists. Their aim is to study the relevant solutions in order to gain insight into nonequilibrium phenomena in spatially extended systems.
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In nonlinear dynamics, very similar equations are called complex Ginzburg-Landau equations.
“The very similar equations that are considered in the context of nonlinear dynamics typically go under the name of complex Ginzburg-Landau equations [76,77].”
From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [77]
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Non-equilibrium Bose–Einstein condensation in photonic systems
Bloch, J., Carusotto, I., & Wouters, M. (2022) · Nature Reviews Physics · doi:10.1038/s42254-022-00464-0 · Cited by 105 · see citing works
How to exploit driving and dissipation to stabilize and manipulate quantum many-body states
Carusotto, I. (2025) · Comptes Rendus. Physique · doi:10.5802/crphys.258 · Cited by 5 · see citing works
“The very similar equations that are investigated in the context of nonlinear dynamics typically go under the name of complex Ginzburg-Landau equations [54, 55].”
- Authors
- Aranson, I. S., & Kramer, L.
- Affiliations
- Argonne National Laboratory (US)
- Venue
- Reviews of Modern Physics
- Publisher
- American Physical Society (APS)
- Published
- 2002-02-04
- Volume
- 74
- Issue
- 1
- Pages
- 99-143
- ISSN
- 0034-6861 (ISSN-L)
- 1539-0756
- OpenAlex
- W2002094651
- Cited by
- 1,941
- References
- 1
- Citations by year
- 2026: 99 · 2025: 119 · 2024: 95 · 2023: 94 · 2022: 87 · 2021: 108 · 2020: 90 · 2019: 93 · 2018: 79 · 2017: 82 · 2016: 70 · 2015: 79 · 2014: 80 · 2013: 77 · 2012: 71
- FWCI
- 64.66
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Reviews of Modern Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Nonlinear Waves and Solitons
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- complex Ginzburg-Landau equation, nonlinear waves, second-order phase transition, superconductivity, superfluidity, Bose-Einstein condensation, liquid crystals, nonequilibrium phenomena, spatially extended systems, exact solutions
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