Skip to main content
SpringerLink
Log in

Scale Competition in Nonlinear Schrödinger Models

  • Conference paper
  • First Online:
Nonlinear Science at the Dawn of the 21st Century

Part of the book series: Lecture Notes in Physics ((LNP,volume 542))

  • 4555 Accesses

Abstract

Three types of nonlinear Schrödinger models with multiple length scales are considered. It is shown that the length-scale competition universally gives rise to new localized stationary states. Multistability phenomena with a controlled switching between stable states become possible.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. R. Bishop, D. Cai, N. Gronbech-Jensen, and M. I. Salkola. In A. R. Bishop, S. Jiménez, and L. Vázquez, editors, Fluctuation phenomena: disorder and nonlinearity, page 316, Singapore, 1995. World Scientific.

    Google Scholar 

  2. O. Bang, J. J. Rasmussen, and P. L. Christiansen. Nonlinearity, 7: 205, 1994.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. P. L. Christiansen, J. C. Eilbeck, and R. D. Parmentier, editors. Future Directions of Nonlinear Dynamics in Physical and Biological Systems. Plenum Press, New York, 1993.

    MATH  Google Scholar 

  4. P. L. Christiansen, Yu. B. Gaididei, M. Johansson, K. O. Rasmussen, D. Usero, and L. Vázquez. Phys. Rev. B, 56: 14407, 1997.

    Article  ADS  Google Scholar 

  5. P. L. Christiansen, Yu. B. Gaididei, K. O. Rasmussen, V. K. Mezentsev, and J. J. Rasmussen. Phys. Rev. B, 54: 900, 1996.

    Article  ADS  Google Scholar 

  6. A. S. Davydov. Theory of Molecular Excitons. Plenum, New York, 1971.

    Google Scholar 

  7. J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott. Physica D, 16: 318, 1985.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  8. S. Georghiou, T. D. Bradrick, A. Philippetis, and J. M. Beechem. Biophysical J., 70: 1909, 1996.

    Article  ADS  Google Scholar 

  9. Yu. B. Gaididei, P. L. Christiansen, K. O. Rasmussen, and M. Johansson. Phys. Rev. B, 55: 13365R, 1997.

    Article  ADS  Google Scholar 

  10. Yu. B. Gaididei, D. Hendriksen, P. L. Christiansen, and K. O. Rasmussen. Phys. Rev. B, 58: 3075, 1998.

    Article  ADS  Google Scholar 

  11. Yu. B. Gaididei, S. F. Mingaleev, P. L. Christiansen, and K. O. Rasmussen. Phys. Rev. E, 55: 6141, 1997.

    Article  ADS  Google Scholar 

  12. H. Hasegawa and Y. Kodama. Solitons in Optical Communications. Claredon Press, Oxford, 1995.

    MATH  Google Scholar 

  13. V. A. Hopkins, J. Keat, G. D. Meegan, T. Zhang, and J. D. Maynard. Phys. Rev. Lett., 76: 1102, 1996.

    Article  ADS  Google Scholar 

  14. M. Johansson, Yu. Gaididei, P. L. Christiansen, and K. O. Rasmussen. Phys. Rev. E, 57: 4739, 1998.

    Article  ADS  Google Scholar 

  15. Yu. S. Kivshar, S. A. Gredeskul, A. Sánchez, and L. Vázquez. Phys. Rev. Lett., 64: 1693, 1990.

    Article  ADS  Google Scholar 

  16. T. Kubota, D. R. Ko, and D. Dobbs. J. Hydronaut., 12: 157, 1978.

    Article  Google Scholar 

  17. O. Krée and C. Soize. Mathematics of random phenomena. Reidel, Dordrecht, 1986.

    Google Scholar 

  18. E. W. Laedke, O. Kluth, and K. H. Spatschek. Phys. Rev. E, 54: 4299, 1996.

    Article  ADS  Google Scholar 

  19. L. D. Landau and E. M. Lifshitz. Statistical Physics. Pergamon Press, London, 1959.

    Google Scholar 

  20. E. W. Laedke, K. H. Spatschek, V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn. Pis’ma Zh. Eksp. Teor. Fiz., 62: 652, 1995. [JETP Lett., 62: 677, 1995].

    ADS  Google Scholar 

  21. E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn. Phys. Rev. Lett., 73: 1055, 1994.

    Article  ADS  Google Scholar 

  22. V. K. Mezentsev, S. L. Musher, I. V. Ryzhenkova, and S. K. Turitsyn. Pis’ma Zh. Eksp. Teor. Fiz., 60: 815, 1994. [JETP Lett., 60: 829, 1994].

    ADS  Google Scholar 

  23. A. C. Newell and J. V. Moloney. Nonlinear Optics. Addison-Wiley, Amsterdam, 1992.

    Google Scholar 

  24. J. J. Rasmussen and K. Rypdal. Phys. Scr., 33: 481, 1986.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  25. K. Rypdal and J. J. Rasmussen. Phys. Scr., 33: 498, 1986.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  26. R. Scharf and A. R. Bishop. Phys. Rev. E, 47: 1375, 1993.

    Article  ADS  Google Scholar 

  27. R. Scharf. Chaos, Solitons and Fractals, 5: 2527, 1995.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  28. A. C. Scott. Phys. Rep., 217: 1, 1992.

    Article  ADS  Google Scholar 

  29. K. H. Spatschek and F. G. Mertens, editors. Nonlinear Coherent Structures in Physics and Biology. Plenum Press, New York, 1994.

    Google Scholar 

  30. C. M. Soukoulis, editor. Photonic Band Gaps and Localization. Plenum Press, New York, 1993.

    Google Scholar 

  31. C. M. Soukoulis, editor. Photonic Band Gap Materials. Kluwer Academic Publishers, Dordrecht / Boston / London, 1996. ed[32]_L. Vázquez, L. Streit, and V. M. Pérez-Garcia, editors. Nonlinear Klein-Gordon and Schrödinger Systems: Theory and Applications. World Scientific, Singapore, 1996.

    Google Scholar 

Download references

Authors
  1. Yu.B. Gaididei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P.L. Christiansen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S.F. Mingaleev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematical Modelling, The Technical University of Denmark, Building 321, 2800, Kgs. Lyngby, Denmark

    P. L. Christiansen , M. P. Sørensen  & A. C. Scott ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gaididei, Y., Christiansen, P., Mingaleev, S. (2000). Scale Competition in Nonlinear Schrödinger Models. In: Christiansen, P.L., Sørensen, M.P., Scott, A.C. (eds) Nonlinear Science at the Dawn of the 21st Century. Lecture Notes in Physics, vol 542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46629-0_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-46629-0_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66918-0

  • Online ISBN: 978-3-540-46629-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation