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

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...

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Bibliographic Details
Published in:Optics letters 2018-08, Vol.43 (15), p.3690-3693
Main Authors: Vasylchenkova, Anastasiia, Prilepsky, Jaroslaw E, Turitsyn, Sergei K
Format: Article
Language:English
Subjects:
Computation
Contours
Eigenvalues
Integrals
Numerical analysis
Random noise
Shape
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Summary: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.
ISSN:0146-9592
1539-4794
DOI:10.1364/OL.43.003690