Contour integrals for numerical computation of discrete eigenvalues in the Zakharov–Shabat problem

Anastasiia Vasylchenkova*, Jaroslaw E. Prilepsky, Sergei K. Turitsyn

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We propose a novel algorithm for the numerical computation of discrete eigenvalues in the Zakharov–Shabat problem. Our approach is based on contour integrals of the nonlinear Fourier spectrum function in the complex plane of the spectral parameter. The reliability and performance of the new approach are examined in application to a single eigenvalue, multiple eigenvalues, and the degenerate breather’s multiple eigenvalue. We also study the impact of additive white Gaussian noise on the stability of numerical eigenvalues computation.

Original languageEnglish
Pages (from-to)3690-3693
Number of pages4
JournalOptics Letters
Volume43
Issue number15
Early online date3 Jul 2018
DOIs
Publication statusPublished - 27 Jul 2018

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eigenvalues
random noise

Bibliographical note

©2018 Optical Society of America]. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.

Cite this

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abstract = "We propose a novel algorithm for the numerical computation of discrete eigenvalues in the Zakharov–Shabat problem. Our approach is based on contour integrals of the nonlinear Fourier spectrum function in the complex plane of the spectral parameter. The reliability and performance of the new approach are examined in application to a single eigenvalue, multiple eigenvalues, and the degenerate breather’s multiple eigenvalue. We also study the impact of additive white Gaussian noise on the stability of numerical eigenvalues computation.",
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Contour integrals for numerical computation of discrete eigenvalues in the Zakharov–Shabat problem. / Vasylchenkova, Anastasiia; Prilepsky, Jaroslaw E.; Turitsyn, Sergei K.

In: Optics Letters, Vol. 43, No. 15, 27.07.2018, p. 3690-3693.

Research output: Contribution to journalArticle

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