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On some localized solutions of coupled Ginzburg-Landau equations

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Instabilities and Nonequilibrium Structures VII & VIII

Part of the book series: Nonlinear Phenomena and Complex Systems ((NOPH,volume 8))

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Abstract

Coupled Complex Ginzburg-Landau equations describe generic features of the dynamics of coupled fields when they are close to instabilities leading to nonlinear oscillations. We study numerically this equation set within a particular range of parameters, and find uniformly propagating localized objects behaving as coherent structures. Some of the localized objects found are interpreted in terms of exact analytical solutions.

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References

  1. M. Cross and P. Hohenberg, Rev. Mod. Phys. 65, 851 (1993), and references therein.

    Article  ADS  Google Scholar 

  2. M. San Miguel, Phys. Rev. Lett. 75, 425 (1995).

    Article  ADS  Google Scholar 

  3. L. Gil, Phys. Rev. Lett. 70, 162 (1993).

    Article  ADS  Google Scholar 

  4. H. Riecke. Localized structures in pattern-forming systems. in Pattern Formation in Continuous and Coupled Systems: a Survey Volume, Ed. by M. Golubitsky, D. Luss, and S.H. Strogatz (Springer, Berlin, 1999).

    Google Scholar 

  5. M. van Hecke, Phys. Rev. Lett. 80, 1896 (1998).

    Article  ADS  Google Scholar 

  6. M. van Hecke, C. Storm, and W. van Saarloos. Physica D 134, 1 (1999).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. R. Montagne, E. Hernández-García, A. Amengual, and M. San Miguel, Phys. Rev. E 56, 151 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  8. E. Hernández-García, M. Hoyuelos, R. Montagne, M. San Miguel, P. Colet, Int. J. Bif. Chaos 9, 2257 (1999).

    Article  Google Scholar 

  9. W. van Saarloos and P. Hohenberg, Physica D 56, 303 (1992), and (Errata) Physica D 69, 209 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. K. Nozaki and N. Bekki, Phys. Rev. Lett. 51, 2171 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  11. K. Nozaki and N. Bekki, J. Phys. Soc. Japan 53, 1581 (1984).

    Article  MathSciNet  ADS  Google Scholar 

  12. K. Kneubüühl and J. Feng, IEEE J. Quantum Electron. 29, 590 (1993).

    Article  ADS  Google Scholar 

  13. R. Conte and M. Musette, Physica D 69, 1 (1993).

    Article  MathSciNet  ADS  MATH  Google Scholar 

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© 2004 Kluwer Academic Publishers

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Montagne, R., Hernández-García, E. (2004). On some localized solutions of coupled Ginzburg-Landau equations. In: Descalzi, O., Martínez, J., Tirapegui, E. (eds) Instabilities and Nonequilibrium Structures VII & VIII. Nonlinear Phenomena and Complex Systems, vol 8. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2149-7_19

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  • DOI: https://doi.org/10.1007/978-1-4020-2149-7_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-015-6994-1

  • Online ISBN: 978-1-4020-2149-7

  • eBook Packages: Springer Book Archive

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