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Two Approaches for Investigation of Soliton Pulse in a Nonlinear Medium

  • I. A. Molotkov
  • N. I. Manaenkova
Part of the NATO Science Series book series (NAII, volume 31)

Abstract

In this paper, we discuss the use of a generalized nonlinear Schrödinger equation
$$ i\psi _x + \psi _{tt} + 2|\psi |^2 \psi - i\beta \psi _{ttt} + i\gamma \left( {|\psi |^2 \psi } \right), = 0, \beta > 0, \gamma > 0 $$
(1)
for the complex amplitude ψ(x,t) of the light guide pulse envelope. The use of the subpicosecond and femtosecond pulses gives one many additional opportunities for light guides devices and, in particular, opportunity to increase transmitted powers. However in the mentioned ranges it is necessary more accurate to take into account nonlinear and dispersion effects. There are serious theoretical arguments [1, 2, 3], that the additional terms with β and γ in (1) permit one to describe transition to the sub- picosecond range. It is necessary to note, that these terms naturally appear under consecutive asymptotic derivation of the equation of type (1) in [4]. The highest nonlinear term was taken into account in [1, 5, 6, 7], and term Ψ m is considered by [6, 7, 8].

Keywords

Cauchy Problem Additional Term Light Guide Nonlinear Schrodinger Equation Soliton Pulse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Anderson, D. and Lisak, M. (1983) Nonlinear asymmetric self-phase modulation and self-steepening of pulses in long optical waveguides, Phys. Rev. A 27, 1393–1398.ADSCrossRefGoogle Scholar
  2. 2.
    Hasegava, A. and Kodama, Y. (1981) Signal transmission by optical solitons in monomode fiber, Proc. IEEE 69, l145–1150.Google Scholar
  3. 3.
    Grudinin, A.B., Men’shov, V.N. and Fursa, T.N. (1990) On femtosecond soliton propagation in monomode fibers JETP 97, 249–251Google Scholar
  4. 4.
    Bisyarin, M.A. and Molotkov, I.A. (1992) Self-action of short pulses in nonhomogeneous graded-index light guids, Opt. and Quant. Electr. 24, 303–312.CrossRefGoogle Scholar
  5. 5.
    Hayata, K. and Koshiba, M. (1994) Bright-kink simbions resulting from the combined effect of self-trapping and intrapulse stimulated Raman scattering, J. Opt. Soc. Amer., ser. B 11, 61–63.ADSCrossRefGoogle Scholar
  6. 6.
    Gromov, E.M. and.Talanov, V.I (1996) Nonlinear dynamics of short wave packets in dispersing media, JETP 110, 137–149.Google Scholar
  7. 7.
    Abdullaev, F.K., S.A.Darmanyan, S.A., Bischoff, S. and Soerensen, P. (1997) Modulational instability of electromagnetics waves in media with varying nonlinearity, J.Opt.Soc.Amer. ser.B 14, 27–33.ADSCrossRefGoogle Scholar
  8. 8.
    Elgin, J.N.(1992) Soliton propagation in an optical fiber with third-order dispersion, Opt. Lett. 17, 1409–1410.Google Scholar
  9. 9.
    Bisyarin, M.A. and Molotkov, I.A. (1996) Finite-amplitude pulses in light guides with quadratic profile of the refractive index, Proc. of the SPIE 2943, 24–31.ADSCrossRefGoogle Scholar
  10. 10.
    Molotkov, I.A. and Vakulenko, S.A. (1988) Concentrated Nonlinear Waves. Pub. Leningrad Univ., Leningrad.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • I. A. Molotkov
    • 1
  • N. I. Manaenkova
    • 1
  1. 1.Institute of Terrestrial Magnetizm, Ionosphere and Radio Wave Propagation Russian Academy of ScienceMoscow RegionRussia

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