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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 172, Number 2, Pages 224–235
DOI: https://doi.org/10.4213/tmf6953 (Mi tmf6953) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Detection and construction of an elliptic solution of the complex cubic–quintic Ginzburg–Landau equation

R. Conteab, Tuen-Wai Ngb

a LRC MESO, Centre de mathématiques et de leurs applications et CEA-DAM, École normale supérieure de Cachan, Cachan, France
b Department of Mathematics, Faculty of Science, The University of Hong Kong, Hong Kong
Full-text PDF (481 kB) Citations (4)
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DOI: https://doi.org/10.4213/tmf6953
Abstract: In evolution equations for a complex amplitude, the equation for the phase is much more intricate than for the amplitude. Nevertheless, general methods should be applicable to both variables. In the example of the traveling-wave reduction of the complex cubic–quintic Ginzburg–Landau (CGL5) equation, we explain how to overcome the difficulties arising in two methods: (1) the criterion that the sum of residues of an elliptic solution is zero and (2) the construction of a first-order differential equation admitting a given equation as a differential consequence (subequation method).
Keywords: elliptic solution, residue criterion, subequation method, complex quintic Ginzburg–Landau equation.
English version:
Theoretical and Mathematical Physics, 2012, Volume 172, Issue 2, Pages 1073–1084
DOI: https://doi.org/10.1007/s11232-012-0096-4
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: R. Conte, Tuen-Wai Ng, “Detection and construction of an elliptic solution of the complex cubic–quintic Ginzburg–Landau equation”, TMF, 172:2 (2012), 224–235; Theoret. and Math. Phys., 172:2 (2012), 1073–1084
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf6953
  • https://doi.org/10.4213/tmf6953
  • https://www.mathnet.ru/eng/tmf/v172/i2/p224
    • This publication is cited in the following 4 articles:
    1. Robert Conte, Micheline Musette, Tuen Wai Ng, Chengfa Wu, “All meromorphic traveling waves of cubic and quintic complex Ginzburg-Landau equations”, Physics Letters A, 481 (2023), 129024  crossref
    2. Gu Y., Wu Ch., Yao X., Yuan W., “Characterizations of All Real Solutions For the Kdv Equation and W-R”, Appl. Math. Lett., 107 (2020), 106446  crossref  mathscinet  isi
    3. Robert Conte, Micheline Musette, Mathematical Physics Studies, The Painlevé Handbook, 2020, 51  crossref
    4. Conte R., Ng T.-W., “Meromorphic traveling wave solutions of the complex cubic-quintic Ginzburg-Landau equation”, Acta Appl. Math., 122:1 (2012), 153–166  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:617
    Full-text PDF :198
    References:59
    First page:19
     
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