We propose a new method for finding discrete eigenvalues for the direct Zakharov-Shabat problem, based on moving in the complex plane along the argument jumps of the function a(ζ), the localization of which does not require great accuracy. It allows to find all discrete eigenvalues taking into account their multiplicity faster than matrix methods and contour integrals. The method shows significant advantage over other methods when calculating a large discrete spectrum, both in speed and accuracy.

Original languageEnglish
Article number105718
JournalCommunications in Nonlinear Science and Numerical Simulation
Publication statusPublished - May 2021


  • Direct scattering transform
  • Nonlinear fourier transform
  • Nonlinear schrödinger equation
  • Zakharov-Shabat problem

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