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

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.

Publication DOI: https://doi.org/10.1364/OL.43.003690
Dataset DOI: https://doi.org/10.17036/researchdata.aston.ac.uk.00000378
Divisions: Engineering & Applied Sciences > Electrical, Electronic & Power Engineering
Engineering & Applied Sciences > Aston Institute of Photonics Technology
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: ©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.
Uncontrolled Keywords: Atomic and Molecular Physics, and Optics
Full Text Link:
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
https://www.osa ... i=ol-43-15-3690 (Publisher URL)
PURE Output Type: Article
Published Date: 2018-07-27
Published Online Date: 2018-07-03
Accepted Date: 2018-07-02
Authors: Vasylchenkova, Anastasiia ( 0000-0002-6997-9427)
Prilepsky, Jaroslaw E. ( 0000-0002-3035-4112)
Turitsyn, Sergei K. ( 0000-0003-0101-3834)

Download

[img]

Version: Accepted Version

| Preview

Export / Share Citation


Statistics

Additional statistics for this record