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Sibirskii Zhurnal Vychislitel'noi Matematiki
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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2020, Volume 23, Number 2, Pages 117–125
DOI: https://doi.org/10.15372/SJNM20200201 (Mi sjvm737) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The numerical solution of the direct Zakharov–Shabat scattering problem

N. I. Gorbenkoab, V. P. Il'inab, A. M. Krylovb, L. L. Fruminca

a Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090 Russia
b Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090 Russia
c Institute of Automation and Electrometry Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 1, Novosibirsk, 630090 Russia
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DOI: https://doi.org/10.15372/SJNM20200201
Abstract: The numerical solution of the direct scattering problem for a system of the Zakharov–Shabat equations is considered. Based on the Marchuk identity, a fourth order method of approximation accuracy is proposed. The numerical simulation of the scattering problem is carried out using an example of two characteristic boundary value problems with known solutions. The calculations have confirmed high accuracy of the algorithm proposed, which is necessary in a number of practical applications for optical and acoustic sensing of media in optics and geophysics applied.
Key words: direct scattering problem, fourth order difference scheme, Marchuk identity.
Funding agency Grant number
Russian Foundation for Basic Research 16-29-15122 офи-м
Russian Science Foundation 17-72-30006
Ministry of Science and Higher Education of the Russian Federation 1201364502 (ЛЛФ)
This work was supported by the Russian Foundation for Basic Research (project no.В 16-29-15122 ofi-m), by the Russian Science Foundation (project no.В 17-72-30006), and by the Ministry of Science and Education of the Russian Federation (project no.В 1201364502 (LLF)).
Received: 29.05.2019
Revised: 24.10.2019
Accepted: 19.12.2019
English version:
Numerical Analysis and Applications, 2020, Volume 13, Issue 2, Pages 95–102
DOI: https://doi.org/10.1134/S1995423920020019
Bibliographic databases:
Document Type: Article
UDC: 53.082.531, 53.082.532, 519.6
Language: Russian
Citation: N. I. Gorbenko, V. P. Il'in, A. M. Krylov, L. L. Frumin, “The numerical solution of the direct Zakharov–Shabat scattering problem”, Sib. Zh. Vychisl. Mat., 23:2 (2020), 117–125; Num. Anal. Appl., 13:2 (2020), 95–102
Citation in format AMSBIB
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\paper The numerical solution of the direct Zakharov--Shabat scattering problem
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\vol 23
\issue 2
\pages 117--125
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\crossref{https://doi.org/10.15372/SJNM20200201}
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\transl
\jour Num. Anal. Appl.
\yr 2020
\vol 13
\issue 2
\pages 95--102
\crossref{https://doi.org/10.1134/S1995423920020019}
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    • This publication is cited in the following 1 articles:
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