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.

© 2018 Optical Society of America

Numerical algorithm with fourth-order accuracy for the direct Zakharov-Shabat problem

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Opt. Lett. 44(9) 2264-2267 (2019)

Conservative multi-exponential scheme for solving the direct Zakharov–Shabat scattering problem

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Opt. Lett. 45(7) 2082-2085 (2020)

Efficient numerical method for solving the direct Zakharov–Shabat scattering problem

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Adaptive trust-region-based algorithm for the discrete eigenvalue evaluation of the direct nonlinear Fourier transform

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Opt. Lett. 47(16) 4195-4198 (2022)

Exponential fourth order schemes for direct Zakharov-Shabat problem

Sergey Medvedev, Irina Vaseva, Igor Chekhovskoy, and Mikhail Fedoruk
Opt. Express 28(1) 20-39 (2020)