Extracting solitons from noisy pulses

Jinglai Li*, William L. Kath

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We describe an iterative method that extracts the underlying soliton from a noisy pulse. The method is formulated as a functional iteration: at each step, the soliton component of the difference between the noisy pulse and the current underlying soliton is determined via soliton perturbation theory; this is then added to the soliton, and the process is repeated. We show that this iteration converges if the perturbation is not too large, and we give the specific types of deviations which most easily cause the iteration to fail to converge. As an example of the method's use, we apply it to obtain improved statistics of the amplitude, phase, frequency, and position of a soliton propagating in an optical fiber in the presence of amplifier noise.

Original languageEnglish (US)
Pages (from-to)577-593
Number of pages17
JournalSIAM Journal on Applied Mathematics
Issue number2
StatePublished - 2012


  • Amplifier noise
  • Functional iteration
  • Nonlinear Schrödinger equation
  • Optical fiber communication system
  • Perturbation theory
  • Soliton

ASJC Scopus subject areas

  • Applied Mathematics

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