### 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.

Original language | English |
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Pages (from-to) | 1647-1656 |

Number of pages | 10 |

Journal | Theoretical and Mathematical Physics |

Volume | 133 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 2002 |

### Keywords

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

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## Cite this

Boscolo, S., Turitsyn, S. K., Novokshenov, V. Y., & Nijhof, J. H. B. (2002). Self-similar parabolic optical solitary waves.

*Theoretical and Mathematical Physics*,*133*(3), 1647-1656. https://doi.org/10.1023/A:1021402024334