Efficient Nonlinear Fourier Transform Algorithms of Order Four on Equispaced Grid

Vishal Vaibhav

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
12 Downloads (Pure)

Abstract

We explore two classes of exponential integrators, in this letter, to design the nonlinear Fourier transform (NFT) algorithms with a convergence order of four on an equispaced grid. The integrating factor-based method in the class of the Runge-Kutta methods yields algorithms with complexity O(N\log2N) (where N is the number of samples of the signal), which have superior accuracy-complexity tradeoff than any of the fast methods known currently. The integrators based on Magnus series expansion, namely, standard and commutator-free Magnus methods yield the algorithms of complexity O(N2) that have superior error behavior than that of the fast methods.

Original languageEnglish
Pages (from-to)1269-1272
JournalIEEE Photonics Technology Letters
Volume31
Issue number15
DOIs
Publication statusPublished - 2019

Keywords

  • Nonlinear Fourier transform
  • Zakharov-Shabat scattering problem

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