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

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Fast eighth-order Padé schemes based on Chebyshev polynomials for the direct Zakharov–Shabat problem. / Medvedev, Sergey ; Chekhovskoy, Igor ; Vaseva, Irina и др.

в: Optics Letters, Том 51, № 21, 2026, стр. 5978-5981.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{9358603bcc1b49919601350fe45c717c,

title = "Fast eighth-order Pad{\'e} schemes based on Chebyshev polynomials for the direct Zakharov–Shabat problem",

abstract = "In this work, we construct fast eighth-order Pad{\'e} 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.",

author = "Sergey Medvedev and Igor Chekhovskoy and Irina Vaseva and Mikhail Fedoruk",

year = "2026",

doi = "10.1364/ol.614226",

language = "English",

volume = "51",

pages = "5978--5981",

journal = "Optics Letters",

issn = "0146-9592",

publisher = "The Optical Society",

number = "21",

}

RIS

TY - JOUR

T1 - Fast eighth-order Padé schemes based on Chebyshev polynomials for the direct Zakharov–Shabat problem

AU - Medvedev, Sergey

AU - Chekhovskoy, Igor

AU - Vaseva, Irina

AU - Fedoruk, Mikhail

PY - 2026

Y1 - 2026

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/105055443466

UR - https://www.mendeley.com/catalogue/773997ad-3c36-38ee-9cc1-2c6622588895/

U2 - 10.1364/ol.614226

DO - 10.1364/ol.614226

M3 - Article

C2 - 42962102

VL - 51

SP - 5978

EP - 5981

JO - Optics Letters

JF - Optics Letters

SN - 0146-9592

IS - 21

ER -

ID: 85045405

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

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