Fast eighth-order Padé schemes based on Chebyshev polynomials for the direct Zakharov-Shabat problem.

Authors

Sergey Medvedev, Igor Chekhovskoy, Irina Vaseva, Mikhail Fedoruk

Published in

Optics letters. Volume 51. Issue 21. Pages 5978-5981. Nov 01, 2026. Epub Sep 30, 2026.

Abstract

In this work, we construct fast eighth-order Padé schemes for the direct Zakharov-Shabat scattering problem. The schemes are based on an eighth-order exponential integrator obtained from the Magnus expansion. A direct extension of the conventional fast representation to the eighth-order case leads to insufficiently accurate results in the considered tests. To overcome this difficulty, we reformulate the spectral dependence through the Joukowski mapping and the Chebyshev polynomial basis. Numerical experiments with chirped hyperbolic secant potentials show improved accuracy of the Chebyshev representation in resolved regimes. Its accuracy and computational cost are compared with direct-Cayley fast schemes for different spectral intervals and scaling parameters.

PMID:
42962102
Bibliographic data and abstract were imported from PubMed on 31 Oct 2026.

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