Soliton phase shift calculation for the Korteweg–de Vries equation

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Several non-linear fluid mechanical processes, such as wave propagation in shallow water, are known to generate solitons: localized waves of translation. Solitons are often hidden in a wave packet at the beginning and only reveal themselves in the far-field. With a special signal processing technique known as the non-linear Fourier transform (NFT), solitons can be detected and characterized before they emerge. In this paper, we present a new algorithm aimed at computing the phase shift of solitons in processes governed by the Korteweg–de Vries (KdV) equation. In numerical examples, the new algorithm is found to perform reliably even in cases where existing algorithms break down.
Original languageEnglish
Pages (from-to)122914-122930
JournalIEEE Access
Issue number1
Publication statusPublished - 2019


  • Korteweg–de Vries (KdV) equation
  • non-linear Fourier transform (NFT)
  • norming constant
  • soliton
  • water wave
  • Eigenvalues and eigenfunctions
  • Solitons
  • Mathematical model
  • Fourier transforms
  • Surface waves
  • Scattering
  • Signal processing algorithms


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