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

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Abstract

The investigation of soliton propagation is of great interest for applications in nonlinear optics and optical transmission systems. Optical communication systems based on soliton techniques can substantially enhance communication bit rates. The fibers used in optical communication are not complitely homogeneous. Random fluctuations in the material properties and the geometric structure of the fiber are expected to have important effects on a nonlinear electromagnetic waves propagation along the fiber. The modulational instability of nonlinear plane waves in fibers with random dispersion and amplification has been investigated in [1]–[3]. The adiabatic dynamics of optical solitons under stochastic perturbations was investigated in [4]–[8]. The soliton parameters were governed by the stochastic Langevin equation with an additive or multiplicative noise. The main purpose of those investigations was to study the adiabtic dynamics of solitons under amplifier noise. In addition to adiabatic dynamics, an important effect is the emission of continuum radiation by solitons in random media.

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References

  1. Abdullaev F. Kh., Pisma JTP 20 (1994) 63–66.

    MathSciNet  Google Scholar 

  2. Abdullaev F. Kh., Darmanyan S. A., Kobyakov A., Lederer F., Phys.Lett. A220 (1996) 213–218.

    Article  Google Scholar 

  3. Abdullaev F. Kh., Darmanyan S., Bishoff S., Soerensen M. P., J.Opt.Soc.Am. B14 (1997) 27–33.

    ADS  Google Scholar 

  4. Abdullaev F. Kh., Darmanyan S. A., Khabibullaev P. K., Optical Solitons, ( Springer, Heidelberg, 1993 ).

    Book  Google Scholar 

  5. Hasegawa A., Kodama Yu., Solitons in Optical Communications, (Oxford UP, Oxford, 1995 ).

    Google Scholar 

  6. Elgin J. N., Opt.Lett. 18 (1993) 10–14.

    Article  ADS  Google Scholar 

  7. Abdullaev F. Kh., JTP Letters 9 (1983) 305–308.

    Google Scholar 

  8. Gordon J. P., Haus H.A., Opt.Lett. 11 (1986) 665–667.

    Article  ADS  Google Scholar 

  9. Gordon J. P., J.Opt.Soc.Am. B9 (1992) 9–19.

    Google Scholar 

  10. Gredeskul S. A., Kivshar Yu. S., Phys.Rep. 216 (1992) 1.

    Article  MathSciNet  ADS  Google Scholar 

  11. Anderson, D. Phys.Rev. A27 (1983) 3135.

    Article  ADS  Google Scholar 

  12. Kuznetsov E. A., Mikhailov A. V., Shimokhin I. A., Physica D87 (1995) 201.

    MathSciNet  ADS  Google Scholar 

  13. Smyth N. F., Picomb A. H., Phys.Rev. E57 (1997) 7231–7238.

    ADS  Google Scholar 

  14. Abdullaev F. Kh., Caputo J. G., Phys.Rev. E58 (1998) n.4.

    Google Scholar 

  15. Abdullaev F. Kh., Baizakov B. B., Phys.Rev. A (1998) submitted.

    Google Scholar 

  16. Abdullaev F. Kh., Abdumalikov A. A., Baizakov B. B., Opt.Commun. 138 (1997) 49–54.

    Article  ADS  Google Scholar 

  17. Abdullaev F. Kh., Baizakov B. B., Umarov B. A. JTP Letters 20 (1994) 23–26.

    Google Scholar 

  18. Fibich G., Papanicolaou G. C., SIAM 58 (1998) 111.

    Google Scholar 

  19. Rassmussen K., Gaididei Yu.B., Bang O., Christiansen P. L., Phys.Lett. A204 (1997) 121–126.

    ADS  Google Scholar 

  20. Abdullaev F. Kh., Caputo J. G., Phys.Rev. 55 (1997) 6061–6071.

    Article  MathSciNet  ADS  Google Scholar 

  21. Abdullaev F. Kh., Bronski J., Papanicolaou G.C., Physica D (1998) submitted.

    Google Scholar 

  22. Okawamari T., Maruta A., Kodama Y., New Trends in Optical Soliton Transmission Systems, ( Kluwer AP, Dodrecht, 1998 ) pp. 245–260

    Book  Google Scholar 

  23. Goldstein H., Classical Mechanics, ( Wiley, New York, 1965 ).

    Google Scholar 

  24. Karpman V., Solov’ev V., Physica D3 (1983) 142–154.

    MathSciNet  Google Scholar 

  25. Abdullaev F. Kh., Caputo J. G., Flytzanis N., Phys.Rev. E50 (1994) 1552–1559.

    ADS  Google Scholar 

  26. Hopkins V. A., et al. Phys.Rev.Lett. 76 (1996) 1102–1105.

    Article  ADS  Google Scholar 

  27. Abdullaev F.Kh., Hensen J.H., Bishoff S., Soerensen M.P. and Smeltnik J.W. J.Opt.Soc.Am. B15 (1998) 2424–2432.

    ADS  Google Scholar 

  28. Hasegawa A., Kodama Yu., Phys.Rev.Lett 66 (1991) 161–164.

    Article  MathSciNet  ADS  MATH  Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Abdullaev, F.K. (1999). Chaotic Dynamics of Optical 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_4

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  • DOI: https://doi.org/10.1007/978-3-662-03807-9_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66314-0

  • Online ISBN: 978-3-662-03807-9

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