Higher order convergent fast nonlinear Fourier transform

Vishal Vaibhav*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

20 Citations (Scopus)
37 Downloads (Pure)


It is demonstrated in this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of computing the discrete eigenvalues, the nonlinear Fourier transform (NFT) algorithm thus obtained has a complexity of O(KN+CpNlog2N) such that the error vanishes as mathop O(N-p) where p ϵ {1,2,3,4} and K is the number of eigenvalues. Such an algorithm can be potentially useful for the recently proposed NFT-based modulation methodology for optical fiber communication. The exposition considers the particular case of the backward differentiation formula (Cp=p3) and the implicit Adams method (Cp=(p-13,p>1) of which the latter proves to be the most accurate family of methods for fast NFT.

Original languageEnglish
Pages (from-to)700-703
JournalIEEE Photonics Technology Letters
Issue number8
Publication statusPublished - 2018

Bibliographical note

Accepted Author Manuscript


  • Nonlinear Fourier transform
  • Zakharov-Shabat scattering problem


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