Theoretical and Mathematical Physics

, Volume 133, Issue 3, pp 1647–1656 | Cite as

Self-Similar Parabolic Optical Solitary Waves

  • S. Boscolo
  • S. K. Turitsyn
  • V. Yu. Novokshenov
  • J. H. B. Nijhof
Article

Abstract

We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.

nonlinear optics self-similarity generation of parabolic pulses 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • S. Boscolo
    • 1
  • S. K. Turitsyn
    • 1
  • V. Yu. Novokshenov
    • 2
  • J. H. B. Nijhof
    • 3
  1. 1.Photonics Research Group, School of Engineering and Applied ScienceAston UniversityBirminghamUK
  2. 2.Ufa Scientific CenterInstitute of MathematicsRAS, UfaRussia
  3. 3.Marconi SolstisStratford-Upon-AvonUK

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