Self-similar parabolic optical solitary waves

Sonia Boscolo*, Sergei K. Turitsyn, V.Yu. Novokshenov, J.H.B. Nijhof

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1647-1656
Number of pages10
JournalTheoretical and Mathematical Physics
Issue number3
Publication statusPublished - Dec 2002


  • generation of parabolic pulses
  • nonlinear optics
  • self-similarity


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