Self-Similar Parabolic Optical Solitary Waves
- Cite this article as:
- Boscolo, S., Turitsyn, S.K., Novokshenov, V.Y. et al. Theoretical and Mathematical Physics (2002) 133: 1647. doi:10.1023/A:1021402024334
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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.