We derive rigorously the Fokker-Planck equation that governs the statistics of soliton parameters in optical transmission lines in the presence of additive amplifier spontaneous emission. We demonstrate that these statistics are generally non-Gaussian. We present exact marginal probability-density functions for soliton parameters for some cases. A WKB approach is applied to describe the tails of the probability-density functions.
Bibliographical note© 2005 Optical Society of America
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- Fokker-Planck equation
- optical solitons
- statistical analysis
- optical fibre communication
- WKB calculations