Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations

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Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations. / Kabanikhin, Sergey ; Shishlenin, Maxim ; Novikov, Nikita и др.

в: Mathematics, Том 11, № 21, 4458, 11.2023.

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

BibTeX

@article{c2288e5657c24fa9833fa665a6939a4e,

title = "Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations",

abstract = "In this paper, we consider the Gelfand–Levitan–Marchenko–Krein approach. It is used for solving a variety of inverse problems, like inverse scattering or inverse problems for wave-type equations in both spectral and dynamic formulations. The approach is based on a reduction of the problem to the set of integral equations. While it is used in a wide range of applications, one of the most famous parts of the approach is given via the inverse scattering method, which utilizes solving the inverse problem for integrating the nonlinear Schrodinger equation. In this work, we present a short historical review that reflects the development of the approach, provide the variations of the method for 1D and 2D problems and consider some aspects of numerical solutions of the corresponding integral equations.",

keywords = "Gelfand–Levitan–Krein–Marchenko equation, inverse coefficient problem, inverse scattering problem",

author = "Sergey Kabanikhin and Maxim Shishlenin and Nikita Novikov and Nikita Prokhoshin",

note = "The work is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.",

year = "2023",

month = nov,

doi = "10.3390/math11214458",

language = "English",

volume = "11",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "21",

}

RIS

TY - JOUR

T1 - Spectral, Scattering and Dynamics: Gelfand–Levitan–Marchenko–Krein Equations

AU - Kabanikhin, Sergey

AU - Shishlenin, Maxim

AU - Novikov, Nikita

AU - Prokhoshin, Nikita

N1 - The work is supported by the Mathematical Center in Akademgorodok under the agreement No. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2023/11

Y1 - 2023/11

N2 - In this paper, we consider the Gelfand–Levitan–Marchenko–Krein approach. It is used for solving a variety of inverse problems, like inverse scattering or inverse problems for wave-type equations in both spectral and dynamic formulations. The approach is based on a reduction of the problem to the set of integral equations. While it is used in a wide range of applications, one of the most famous parts of the approach is given via the inverse scattering method, which utilizes solving the inverse problem for integrating the nonlinear Schrodinger equation. In this work, we present a short historical review that reflects the development of the approach, provide the variations of the method for 1D and 2D problems and consider some aspects of numerical solutions of the corresponding integral equations.

AB - In this paper, we consider the Gelfand–Levitan–Marchenko–Krein approach. It is used for solving a variety of inverse problems, like inverse scattering or inverse problems for wave-type equations in both spectral and dynamic formulations. The approach is based on a reduction of the problem to the set of integral equations. While it is used in a wide range of applications, one of the most famous parts of the approach is given via the inverse scattering method, which utilizes solving the inverse problem for integrating the nonlinear Schrodinger equation. In this work, we present a short historical review that reflects the development of the approach, provide the variations of the method for 1D and 2D problems and consider some aspects of numerical solutions of the corresponding integral equations.

KW - Gelfand–Levitan–Krein–Marchenko equation

KW - inverse coefficient problem

KW - inverse scattering problem

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85176336017&origin=inward&txGid=4ccd712e5cef791b209a5ad721300718

UR - https://www.mendeley.com/catalogue/130905b9-d504-33f9-8382-0de5d1e67624/

U2 - 10.3390/math11214458

DO - 10.3390/math11214458

M3 - Article

VL - 11

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 21

M1 - 4458

ER -

ID: 59285263