Self-Similar Parabolic Optical Solitary Waves
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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.
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- Self-Similar Parabolic Optical Solitary Waves
Theoretical and Mathematical Physics
Volume 133, Issue 3 , pp 1647-1656
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- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- nonlinear optics
- generation of parabolic pulses
- Author Affiliations
- 1. Photonics Research Group, School of Engineering and Applied Science, Aston University, Birmingham, UK
- 2. Ufa Scientific Center, Institute of Mathematics, RAS, Ufa, Russia
- 3. Marconi Solstis, Stratford-Upon-Avon, UK