The World of the Complex Ginzburg-Landau Equation

Igor Aranson; Lorenz Kramer

RECORD

The World of the Complex Ginzburg-Landau Equation

Igor Aranson, Lorenz Kramer

Statistical Mechanics · Submitted 6 Jun 2001

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

how it is stated · asserted 1.00 read the record →

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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,633 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.03 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

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. Our goal is to give an overview of various phenomena described the complex Ginzburg-Landau equation in one, two and three dimensions from the point of view of condensed matter physicists. Our approach is to study the relevant solutions to get an insight into nonequilibrium phenomena in spatially extended systems.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear equations in the physics community.	background 1.00	0.03	0.03	asserted 1.00
s1	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.	background 1.00	0.03	0.04	asserted 1.00
s2	Our goal is to give an overview of various phenomena described the complex Ginzburg-Landau equation in one, two and three dimensions from the point of view of condensed matter physicists.	contribution 0.98	0.27	0.07	asserted 0.74
s3	Our approach is to study the relevant solutions to get an insight into nonequilibrium phenomena in spatially extended systems.	method 0.94	0.49	0.05	asserted 0.82

What kind of paper the classifier reports this is: review 1.00 · evidence from literature 0.77.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

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. Our goal is to give an overview of various phenomena described the complex Ginzburg-Landau equation in one, two and three dimensions from the point of view of condensed matter physicists. Our approach is to study the relevant solutions to get an insight into nonequilibrium phenomena in spatially extended systems.

Human review

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References

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

On elliptic solutions of the quintic complex one-dimensional Ginzburg-Landau equation
nlin.PS 2006-02 conditional novelty 7.0 of 10

The paper derives necessary conditions for elliptic wave solutions of the quintic complex Ginzburg-Landau equation and constructs a family of such solutions for coefficients satisfying those conditions.
Singularity methods for meromorphic solutions of differential equations
nlin.SI 2018-06 unverdicted novelty 2.0 of 10

A tutorial presenting singularity-analysis methods that classify all meromorphic solutions of autonomous algebraic ODEs, demonstrated on the Kuramoto-Sivashinsky and complex Ginzburg-Landau equations.

How later papers used it

111 later papers cite it

Evidence: substantial. 110 of the citing papers share no author with it, and 11 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 172 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

2 later papers by other authors are listed below: 2 used its method or tool.

Uses its method or tool 2 of 6 papers with this label

Followed this paper by perturbing stripes with its ansatz, collecting terms, solving for the growth rate, and expanding in the wavenumber to obtain the growth rate.

Transverse modulational dynamics of quenched patterns (2023) · 0.94 · paraphrased: the licence does not allow quoting
Followed the steps given in this paper, where the stability of planar wave solutions was studied, to determine this value.

Global attractors and extinction dynamics of cyclically competing species (2013) · 0.99 · paraphrased: the licence does not allow quoting

How the literature uses it

7 arXiv papers cite this in 7 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 2 sentences without a confident label

Cites it as background 5 papers

The complex Ginzburg-Landau equation (CGLE) became a widely used physical-mathematical model appearing in many branches of physics, chemistry and biology, in order to describe various localized structures [ref] .

Ginzburg-Landau equation for dynamical four-wave mixing in gain nonlinear media with relaxation · Introduction · 0.99
For a summary of results on CGL5, see the reviews [ref] .

Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation · Introduction. Modulus vs. phase in amplitude equations · 1.00
These phenomena include pattern formation, spatio-temporal intermittency, superconductivity, nonlinear optics, Bose-Einstein condensation, etc, see the reviews [ref] .

New solutions to the complex Ginzburg-Landau equations · Introduction · 1.00

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