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Localized self-similar structures for a coupled nls equation: An approximate analysis

  • Part VI: Mathematical Methods
  • Conference paper
  • First Online:
Nonlinear Coherent Structures in Physics and Biology

Part of the book series: Lecture Notes in Physics ((LNP,volume 393))

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Abstract

We perform an approximate analysis of some particular self-similar solutions of the (2+1)-dimensional coupled nonlinear Schrödinger equation. These solutions are invariant under a point-symmetry subgroup of the model that involves the Schrödinger conformal symmetry. We use a variational approach to classify them and to determine their approximate structures.

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References

  1. N. B. Abraham and W. J. Firth, J. Opt. Soc. Am. B 7, 951 (1990)

    Google Scholar 

  2. P. D. Maker and R. W. Terhune, Phys.Rev. A 137, 801 (1965)

    Article  Google Scholar 

  3. A. E. Kaplan, Opt. Lett. 8, 560 (1983)

    Google Scholar 

  4. W. J. Firth, A. Fitzgerald and C. Paré, J. Opt. Soc. Am B 7, 1087 (1990)

    Google Scholar 

  5. P. Olver, Applications of Lie Groups to Differential Equations (Springer, Berlin, 1986)

    Google Scholar 

  6. E. L. Ince, Ordinary Differential Equations (Dover, New York, 1956)

    Google Scholar 

  7. F. J. Bureau, Ann. Mat. Pura Appl. IV 41, 163 (1972)

    Google Scholar 

  8. D. Anderson, Phys. Scr. 18, 35 (1978)

    Google Scholar 

  9. L. Gagnon and C. Paré, J. Opt. Soc. Am. A 8, 601 (1991)

    Google Scholar 

  10. J. H. Marburger and F. S. Felber, Phys. Rev. A 17, 335 (1978)

    Google Scholar 

  11. R. Y. Chiao, E. Garmire and C. H. Townes, Phys. Rev. Lett 13, 479 (1964)

    Google Scholar 

  12. D. Pohl, Opt. Commun. 2, 305 (1970)

    Google Scholar 

  13. J. J. Rasmussen and K. Rypdal, Physica Scripta 33, 481 (1986); K. Rypdal and J. J. Rasmussen, Physica Scripta 33, 498 (1986)

    Google Scholar 

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Authors and Affiliations

  1. Centre d'Optique Photonique et Laser, GIK 7P4, Ste-Foy, Québec, Canada

    L. Gagnon

Authors
  1. L. Gagnon
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Editor information

M. Remoissenet M. Peyrand

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© 1991 Springer-Verlag

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Gagnon, L. (1991). Localized self-similar structures for a coupled nls equation: An approximate analysis. In: Remoissenet, M., Peyrand, M. (eds) Nonlinear Coherent Structures in Physics and Biology. Lecture Notes in Physics, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54890-4_194

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  • DOI: https://doi.org/10.1007/3-540-54890-4_194

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54890-4

  • Online ISBN: 978-3-540-46458-7

  • eBook Packages: Springer Book Archive

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