Standard

On the combined method for solving the inverse problem of the Zakharov–Shabat system. / Medvedev, S. B.; Vaseva, I. A.; Fedoruk, M. P.

In: Physica D: Nonlinear Phenomena, Vol. 483, 134942, 12.2025.

Research output: Contribution to journal › Article › peer-review

Harvard

Medvedev, SB, Vaseva, IA & Fedoruk, MP 2025, 'On the combined method for solving the inverse problem of the Zakharov–Shabat system', Physica D: Nonlinear Phenomena, vol. 483, 134942. https://doi.org/10.1016/j.physd.2025.134942

APA

Medvedev, S. B., Vaseva, I. A., & Fedoruk, M. P. (2025). On the combined method for solving the inverse problem of the Zakharov–Shabat system. Physica D: Nonlinear Phenomena, 483, [134942]. https://doi.org/10.1016/j.physd.2025.134942

Vancouver

Medvedev SB, Vaseva IA, Fedoruk MP. On the combined method for solving the inverse problem of the Zakharov–Shabat system. Physica D: Nonlinear Phenomena. 2025 Dec;483:134942. doi: 10.1016/j.physd.2025.134942

Author

Medvedev, S. B. ; Vaseva, I. A. ; Fedoruk, M. P. / On the combined method for solving the inverse problem of the Zakharov–Shabat system. In: Physica D: Nonlinear Phenomena. 2025 ; Vol. 483.

BibTeX

@article{df8462332f304959b0b9024549bc324a,
title = "On the combined method for solving the inverse problem of the Zakharov–Shabat system",
abstract = "We study the combined method for solving the inverse problem of the Zakharov–Shabat system associated with the nonlinear Schr{\"o}dinger equation. The method is based on a high-precision algorithm for the Gelfand–Levitan–Marchenko equation for a continuous spectrum and the Darboux method for a discrete spectrum. A comparison of the combined Darboux method and the GLME-based algorithm is made.",
keywords = "Darboux method, Gelfand–Levitan–Marchenko equation, Inverse scattering transform, Inverse spectral problem, Nonlinear Fourier transform, Toeplitz Inner-Bordering method, Zakharov–Shabat system",
author = "Medvedev, {S. B.} and Vaseva, {I. A.} and Fedoruk, {M. P.}",
note = "The work of S.B. Medvedev and M.P. Fedoruk was supported by the RSF, Russia grant 25-61-00010, https://rscf.ru/project/25-61-00010/. The work of I.A. Vaseva was supported by the state assignment of Ministry of Science and Higher Education of the Russian Federation for Federal Research Center for Information and Computational Technologies On the combined method for solving the inverse problem of the Zakharov–Shabat system / S. B. Medvedev, I. A. Vaseva, M. P. Fedoruk // Physica D: Nonlinear Phenomena. - 2025. - Т. 483. - С. 134942. DOI: 10.1016/j.physd.2025.134942 ",
year = "2025",
month = dec,
doi = "10.1016/j.physd.2025.134942",
language = "English",
volume = "483",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier Science Publishing Company, Inc.",

}

RIS

TY - JOUR

T1 - On the combined method for solving the inverse problem of the Zakharov–Shabat system

AU - Medvedev, S. B.

AU - Vaseva, I. A.

AU - Fedoruk, M. P.

N1 - The work of S.B. Medvedev and M.P. Fedoruk was supported by the RSF, Russia grant 25-61-00010, https://rscf.ru/project/25-61-00010/. The work of I.A. Vaseva was supported by the state assignment of Ministry of Science and Higher Education of the Russian Federation for Federal Research Center for Information and Computational Technologies On the combined method for solving the inverse problem of the Zakharov–Shabat system / S. B. Medvedev, I. A. Vaseva, M. P. Fedoruk // Physica D: Nonlinear Phenomena. - 2025. - Т. 483. - С. 134942. DOI: 10.1016/j.physd.2025.134942

PY - 2025/12

Y1 - 2025/12

N2 - We study the combined method for solving the inverse problem of the Zakharov–Shabat system associated with the nonlinear Schrödinger equation. The method is based on a high-precision algorithm for the Gelfand–Levitan–Marchenko equation for a continuous spectrum and the Darboux method for a discrete spectrum. A comparison of the combined Darboux method and the GLME-based algorithm is made.

AB - We study the combined method for solving the inverse problem of the Zakharov–Shabat system associated with the nonlinear Schrödinger equation. The method is based on a high-precision algorithm for the Gelfand–Levitan–Marchenko equation for a continuous spectrum and the Darboux method for a discrete spectrum. A comparison of the combined Darboux method and the GLME-based algorithm is made.

KW - Darboux method

KW - Gelfand–Levitan–Marchenko equation

KW - Inverse scattering transform

KW - Inverse spectral problem

KW - Nonlinear Fourier transform

KW - Toeplitz Inner-Bordering method

KW - Zakharov–Shabat system

UR - https://www.mendeley.com/catalogue/526e7b1c-e45f-37ae-a283-ada7b038547a/

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105016809751&origin=inward

U2 - 10.1016/j.physd.2025.134942

DO - 10.1016/j.physd.2025.134942

M3 - Article

VL - 483

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

M1 - 134942

ER -

ID: 69976866