| Dublin Core |
PKP Metadata Items |
Metadata for this Document |
| 1. |
Title |
Title of document |
A “SUPER-FAST” ALGORITHM FOR SOLVING THE DIRECT SCATTERING PROBLEM FOR THE MANAKOV SYSTEM |
| 2. |
Creator |
Author's name, affiliation, country |
L. L. Frumin; Institute of Automation and Electrometry, SB RAS |
| 2. |
Creator |
Author's name, affiliation, country |
A. E. Chernyavsky; Institute of Automation and Electrometry, SB RAS |
| 2. |
Creator |
Author's name, affiliation, country |
O. V. Belay; Institute of Automation and Electrometry, SB RAS |
| 3. |
Subject |
Discipline(s) |
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| 3. |
Subject |
Keyword(s) |
Schrodinger equation; Manakov system; direct scattering problem; transfer matrix; convolution; Fourier transform |
| 4. |
Description |
Abstract |
The construction of an accelerated algorithm for solving the direct scattering problem for the continuous spectrum of the Manakov system associated with the vector nonlinear Schrodinger equation of the Manakov model is considered. The numerical formulation of the problem leads to the problem of quickly calculating the products of polynomials dependent on the spectral parameter of the problem. For localized solutions, the so-called “super-fast” algorithm for solving the direct scattering problem of the second order of accuracy is presented, based on the convolution theorem and the fast Fourier transform, which requires asymptotically only (︀ Log2 )︀ arithmetic operations for a discrete grid of size . To speed up the calculation of the reflection coefficient spectra, a matrix variant of the fast Fourier transform is proposed and tested, when the coefficients of a series of discrete Fourier transforms are non-commuting matrices. Numerical simulation using the example of the exact solution of the Manakov system (hyperbolic secant) confirmed the high calculation speed and the second order of accuracy of the algorithm approximation. |
| 5. |
Publisher |
Organizing agency, location |
The Russian Academy of Sciences |
| 6. |
Contributor |
Sponsor(s) |
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| 7. |
Date |
(DD-MM-YYYY) |
15.12.2024
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| 8. |
Type |
Status & genre |
Peer-reviewed Article |
| 8. |
Type |
Type |
Research Article |
| 9. |
Format |
File format |
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| 10. |
Identifier |
Uniform Resource Identifier |
https://consilium.orscience.ru/0044-4669/article/view/669687 |
| 10. |
Identifier |
Digital Object Identifier (DOI) |
10.31857/S0044466924120143 |
| 10. |
Identifier |
eLIBRARY Document Number (EDN) |
KBMEIL |
| 11. |
Source |
Title; vol., no. (year) |
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki; Vol 64, No 12 (2024) |
| 12. |
Language |
English=en |
ru |
| 13. |
Relation |
Supp. Files |
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| 14. |
Coverage |
Geo-spatial location, chronological period, research sample (gender, age, etc.) |
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| 15. |
Rights |
Copyright and permissions |
Copyright (c) 2024 Russian Academy of Sciences
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