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Perturbative Studies of the Zakharov-Shabat Scattering Problem

  • Z. V. Lewis
  • J. N. Elgin
  • K. J. Blow
  • N. J. Doran
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 30)

Abstract

Optical pulse propagation through monomode fibres is described by the nonlinear Schrödinger equation (NLS)[1–3]. For an ideal system this takes the form
$$i{q_t} + {q_{xx}} + q{\left| q \right|^2} = 0$$
(1)
with q a known function at t=0. In practice, equation 1 must be modified to incorporate other effects such as loss or stimulated scattering. Also, q may not be well-defined. For example, the laser source producing the optical pulse input to the fibre may not be bandwidth limited resulting in a frequency chirped input pulse. The nature of the chirp may be known or stochastic in the sense that there is a random phase variation along the pulse. It is clearly desirable to know how such effects modify the scattering data, since they will directly affect the properties of the optical solitons.

Keywords

Optical Soliton Optical Pulse Propagation Order Shift Perturbative Study Optical Pulse Input 
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

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    V.E. Zakharov and A.B. Shabat, Sov. Phys. JETP 34, 62 (1972)Google Scholar
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    M.J. Ablowitz, D.J. Kaup, A.C. Newell and H.Segur, SIAM 53, 249 (1974)Google Scholar
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    J. Satsuma and N. Yajima, Suppl. Prog. Theor. Phys. 55, 284 (1974)CrossRefGoogle Scholar
  4. 4.
    J.N. Elgin and D.J. Kaup, Opt. Commun. 43, 233 (1982-T- Google Scholar
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    V.E. Zakharov, Funktional’nyi Analiz i Ego Prilozheniya 14, 15 (1980)Google Scholar
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    V.E. Zakharov, Physica 3D (1981)Google Scholar
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    N.J. Doran and K.J. Blow, IEEE J. Quant Elec. QE19, 1883 (1983)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Z. V. Lewis
    • 1
  • J. N. Elgin
    • 1
  • K. J. Blow
    • 2
  • N. J. Doran
    • 2
  1. 1.Department of MathematicsImperial CollegeLondonGreat Britain
  2. 2.British Telecom Research LaboratoriesMartlesham HeathIpswich SuffolkGreat Britain

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