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Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation

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Robert Conte (LRC MESO, ENS Cachan), Tuen-Wai Ng (The University of Hong Kong)

Classical Analysis and ODEs · Submitted 13 Apr 2012

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

The authors' main claim Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic.

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arXiv ID1204.3032 (version 1)
Pith ID27QJFUUE, Pith's permanent record of this paper and its review
CitationENS Cachan), Robert Conte (LRC MESO, Tuen-Wai Ng (The University of Hong Kong). "Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation." arXiv:1204.3032 (2012). https://pith.science/paper/27QJFUUE
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,934 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.60 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. contribution 0.75 0.86 0.05 asserted 0.78
s1 Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. result 0.70 0.93 0.38 asserted 1.00
s2 We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method. contribution 0.83 0.84 0.22 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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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

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie's lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.

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References
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5 arXiv papers cite this in 18 sentences

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Papers citing it · 15 sentences without a confident label

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Cites it as support 1 paper
  • Indeed, as proven in [ref] , the number of Laurent series of $M$ is finite (and equal to $2$ or $4$), therefore the number of admissible Hermite decompositions of $M$ is finite, and so is the number of solutions $M$ in the elliptic or degenerate elliptic class.

    Singularity methods for meromorphic solutions of differential equations · All admissible partial fraction decompositions · 0.99

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