Skip to main content

Part of the book series: Centre de Physique des Houches ((LHWINTER,volume 12))

Abstract

The main aim of this article is to demonstrate two methods for investigating the stability of solitons. We restrict ourselves to consideration of two basic models, namely, the nonlinear Schrodinger equation (NLSE) and the three-wave system. Both systems have a lot of applications in optics.

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

Access this chapter

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

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.Hasegawa and F.Tappet, Appl.Phys.Lett. 23, 142 (1973).

    Article  ADS  Google Scholar 

  2. G.P. Agrawal, Nonlinear Fiber Optics, ( Academic Press, New York, 1989 ).

    Google Scholar 

  3. E.A.Kuznetsov, A.M.Rubenchik and V.E.Zakharov, Phys. Rep. 142, 103 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  4. N.Bloembergen, Nonlinear Optics (Benjamin Inc., N.Y., Amsterdam, 1965 ).

    Google Scholar 

  5. Yu. N.Karamzin and A.P.Sukhorukov, JETP, 68, 634 (1975)

    Google Scholar 

  6. Yu. N.Karamzin and A.P.Sukhorukov, JETP Letters, 20, 734 (1974) (both in Russian).

    Google Scholar 

  7. V.E.Zakharov and E.A.Kuznetsov, UFN (Physics Uspekhi), 167, 1137 (1997) (in Russian).

    Article  Google Scholar 

  8. V.E.Zakharov and S.V.Manakov, Pis’ma ZhETF (JETP Letters), 18, 413 (1973) (in Russian).

    Google Scholar 

  9. V.E.Zakharov, S.V.Manakov, S.P.Novikov and L.P.Pitaevsky, Theory of Solitons ( Consultants Bureau, New York, 1984 ).

    MATH  Google Scholar 

  10. A.A.Kanashev and A.M.Rubenchik, Physica 4D, 122 (1981).

    ADS  Google Scholar 

  11. G.Derrick, J. Math. Phys., 5, 252 (1966).

    MathSciNet  Google Scholar 

  12. T.B.Benjamin, Proc. Roy. Soc. London, A 328, 153 (1972).

    MathSciNet  ADS  Google Scholar 

  13. V.E.Zakharov and E.A.Kuznetsov, JETP, 39, 285, (1974).

    ADS  Google Scholar 

  14. E.A.Kuznetsov, J.J.Rasmussen and E.G.Shapiro, (in preparation)

    Google Scholar 

  15. E.A.Kuznetsov, Chaos, 6, 381–390 (1996).

    Article  ADS  Google Scholar 

  16. L.Berge, O.Bang, J.J.Rasmussen and V.K,Mezentsev, Phys. Rev. E, 55, 3555 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  17. N.G.Vakhitov and A.A.Kolokolov, Radiofizika, 16, 1020 (1973).

    Google Scholar 

  18. O.A.Ladyzhenskaya, Mathematical Problems of Dynamics of a Viscous Incompressible Fluid, Fizmatgiz, Moscow (1961) (in Russian).

    Google Scholar 

  19. L.Neirenberg, Ann. Sci. Norm. Sup. Pisa, 20, No. 4, 73 (1966).

    Google Scholar 

  20. M.I. Weinstein. Commun Math. Phys. 87, 567 (1983).

    Article  ADS  MATH  Google Scholar 

  21. S.K.Turitsyn, Pis’ma ZhETF (JETP Letters), 61, 458 (1995).

    Google Scholar 

  22. E.A.Kuznetsov and V.E.Zakharov, in book: Nonlinear science at the down of 21st century,ed. P.Christiansen and M. Soerensen, Springer (1999) (in press).

    Google Scholar 

  23. Y. Chen, Phys. Lett., A 234, 443 (1997).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kuznetsov, E.A. (1999). Stability of Solitons. In: Zakharov, V.E., Wabnitz, S. (eds) Optical Solitons: Theoretical Challenges and Industrial Perspectives. Centre de Physique des Houches, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03807-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-03807-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66314-0

  • Online ISBN: 978-3-662-03807-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics