Higher order exponential splittings for the fast Non-linear Fourier Transform of the Korteweg-De Vries equation

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

7 Citations (Scopus)
26 Downloads (Pure)

Abstract

Non-linear Fourier Transforms (NFTs) enable the analysis of signals governed by certain non-linear evolution equations in a way that is analogous to how the conventional Fourier transform is used to analyse linear wave equations. Recently, fast numerical algorithms have been derived for the numerical computation of certain NFTs. In this paper, we are primarily concerned with fast NFTs with respect to the Korteweg-de Vries equation (KdV), which describes e.g. the evolution of waves in shallow water. We find that in the KdV case, the fast NFT can be more sensitive to numerical errors caused by an exponential splitting. We present higher order splittings that reduce these errors and are compatible with the fast NFT. Furthermore we demonstrate for the NSE case that using these splittings can make the accuracy of the fast NFT match that of the conventional NFT.
Original languageEnglish
Title of host publicationProceedings 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
Place of PublicationPiscataway, NJ, USA
PublisherIEEE
Pages4524-4528
ISBN (Electronic)978-1-5386-4658-8, 978-1-5386-4657-1
ISBN (Print)978-1-5386-4659-5
DOIs
Publication statusPublished - 2018
Event2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018: Signal Processing and Artificial Intelligence: Changing the World - Calgary Telus Convention Center (CTCC), Calgary, Canada
Duration: 15 Apr 201820 Apr 2018
https://2018.ieeeicassp.org

Conference

Conference2018 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2018
CountryCanada
CityCalgary
Period15/04/1820/04/18
Internet address

Keywords

  • Fourier transforms
  • Differential equations
  • Signal processing algorithms
  • Boundary conditions
  • Scattering
  • Computational complexity
  • Europe
  • Non-linear Fourier transform
  • exponential splittings
  • Korteweg-de Vries equation

Fingerprint Dive into the research topics of 'Higher order exponential splittings for the fast Non-linear Fourier Transform of the Korteweg-De Vries equation'. Together they form a unique fingerprint.

  • Cite this

    Prins, P. J., & Wahls, S. (2018). Higher order exponential splittings for the fast Non-linear Fourier Transform of the Korteweg-De Vries equation. In Proceedings 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (pp. 4524-4528). IEEE. https://doi.org/10.1109/ICASSP.2018.8461708