Exponential fourth order schemes for direct Zakharov-Shabat problem

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8 Citations (Scopus)

Abstract

Nowadays, improving the accuracy of computational methods to solve the initial value problem of the Zakharov-Shabat system remains an urgent problem in optics. In particular, increasing the approximation order of the methods is important, especially in problems where it is necessary to analyze the structure of complex waveforms. In this work, we propose two finite-difference algorithms of fourth order of approximation in the time variable. Both schemes have the exponential form and conserve the quadratic invariant of Zakharov-Shabat system. The second scheme allows applying fast algorithms with low computational complexity (fast nonlinear Fourier transform).

Original languageEnglish
Pages (from-to)20-39
Number of pages20
JournalOptics Express
Volume28
Issue number1
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • NONLINEAR FOURIER-TRANSFORM
  • DIRECT SCATTERING TRANSFORM
  • INVERSE SYNTHESIS
  • TRANSMISSION
  • MODULATION
  • ALGORITHMS
  • COMPUTATION
  • ACCURACY
  • STANDARD

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