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Pattern Formation Under a Localized Gain

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Book cover Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Part of the book series: Progress in Optical Science and Photonics ((POSP,volume 1))

Abstract

The onset of patterns due to a localized gain is studied analytically in the framework of a real or complex amplitude equation. The instability modes are found, and the bifurcation of small localized solutions is analyzed. Some exact solutions are also found.

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References

  1. B.A. Malomed, Phys. Rev. E 47, R2257 (1993)

    Article  ADS  Google Scholar 

  2. B.A. Malomed, Phys. Rev. E 50, 4249 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  3. S.I. Abarzhi, O. Desjardins, A. Nepomnyashchy, H. Pitsch, Phys. Rev. E 75, 046208 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  4. A. Nepomnyashchy, S.I. Abarzhi, Phys. Rev. E 81, 037202 (2010)

    Article  ADS  Google Scholar 

  5. C.-.K. Lam, B.A. Malomed, K.W. Chow, P.K.A. Wai, Eur. Phys. J. Special Topics 173, 233 (2009)

    Article  ADS  Google Scholar 

  6. Y.V. Kartashov, V.V. Konotop, V.A. Vysloukh, Europhys. Lett. 91, 34003 (2010)

    Google Scholar 

  7. Y.V. Kartashov, V.V. Konotop, V.A. Vysloukh, L. Torner, Opt. Lett. 35, 1638 (2010)

    Article  ADS  Google Scholar 

  8. Y.V. Kartashov, V.V. Konotop, V.A. Vysloukh, L. Torner, Opt. Lett. 35, 3177 (2010)

    Article  ADS  Google Scholar 

  9. Y.V. Kartashov, V.V. Konotop, V.A. Vysloukh, Opt. Lett. 36, 82 (2011)

    Article  ADS  Google Scholar 

  10. V.E. Lobanov, Y.V. Kartashov, V.A. Vysloukh, L. Torner, Opt. Lett. 36, 85 (2011)

    Article  Google Scholar 

  11. D.A. Zezyulin, Y.V. Kartashov, V.V. Konotop, Opt. Lett. 36, 1200 (2011)

    Article  ADS  Google Scholar 

  12. O.V. Borovkova, V.E. Lobanov, Y.V. Kartashov, L. Torner, Opt. Lett. 36, 1936 (2011)

    Article  Google Scholar 

  13. Y.V. Kartashov, V.V. Konotop, V.A. Vysloukh, Opt. Lett. 83, 041806(R) (2011)

    Google Scholar 

  14. C.H. Tsang, B.A. Malomed, C.K. Lam, K.W. Chow, Eur. Phys. J. D 59, 81 (2010)

    Article  ADS  Google Scholar 

  15. O.V. Borovkova, V.E. Lobanov, B.A. Malomed, Europhys. Lett. 97, 44003 (2012)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Technion—Israel Institute of Technology, 32000, Haifa, Israel

    Alexander A. Nepomnyashchy

  2. Minerva Center for Nonlinear Physics of Complex Systems, Technion—Israel Institute of Technology, 32000, Haifa, Israel

    Alexander A. Nepomnyashchy

Authors
  1. Alexander A. Nepomnyashchy
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Correspondence to Alexander A. Nepomnyashchy .

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Editors and Affiliations

  1. Faculty of Engineering The Iby and Aladar Fleischman, Tel Aviv University, Ramat Aviv, Israel

    Boris A. Malomed

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Nepomnyashchy, A.A. (2013). Pattern Formation Under a Localized Gain. In: Malomed, B. (eds) Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations. Progress in Optical Science and Photonics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10091_2012_26

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  • DOI: https://doi.org/10.1007/10091_2012_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21206-2

  • Online ISBN: 978-3-642-21207-9

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