Inverse scattering transform algorithm for the Manakov system
A numerical algorithm is described for solving the inverse spectral scattering problem associated with the Manakov model of the vector nonlinear Schrödinger equation. This model of wave processes simultaneously considers dispersion, nonlinearity and polarization effects. It is in demand in nonlinear...
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| Format: | Article |
| Language: | English |
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Samara National Research University
2023-12-01
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| Series: | Компьютерная оптика |
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| Online Access: | https://www.computeroptics.ru/eng/KO/Annot/KO47-6/470602e.html |
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| author | A.E. Chernyavsky L.L. Frumin |
| author_facet | A.E. Chernyavsky L.L. Frumin |
| author_sort | A.E. Chernyavsky |
| collection | DOAJ |
| description | A numerical algorithm is described for solving the inverse spectral scattering problem associated with the Manakov model of the vector nonlinear Schrödinger equation. This model of wave processes simultaneously considers dispersion, nonlinearity and polarization effects. It is in demand in nonlinear physical optics and is especially perspective for describing optical radiation propagation through the fiber communication lines. In the presented algorithm, the solution to the inverse scattering problem based on the inversion of a set of nested matrices of the discretized system of Gelfand–Levitan–Marchenko integral equations, using a block version of the Levinson-type Toeplitz bordering algorithm. Numerical tests carried out by comparing calculations with known exact analytical solutions confirm the stability and second order of accuracy of the proposed algorithm. We also give an example of the algorithm application to simulate the collision of a differently polarized pair of Manakov optical vector solitons. |
| format | Article |
| id | doaj-art-8dcf2ffe38484c9a9f93b364ac02167e |
| institution | Kabale University |
| issn | 0134-2452 2412-6179 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj-art-8dcf2ffe38484c9a9f93b364ac02167e2025-01-23T09:25:30ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792023-12-0147685686210.18287/2412-6179-CO-1298Inverse scattering transform algorithm for the Manakov systemA.E. Chernyavsky0L.L. Frumin1Institute of Automation and Electrometry SB RASInstitute of Automation and Electrometry SB RASA numerical algorithm is described for solving the inverse spectral scattering problem associated with the Manakov model of the vector nonlinear Schrödinger equation. This model of wave processes simultaneously considers dispersion, nonlinearity and polarization effects. It is in demand in nonlinear physical optics and is especially perspective for describing optical radiation propagation through the fiber communication lines. In the presented algorithm, the solution to the inverse scattering problem based on the inversion of a set of nested matrices of the discretized system of Gelfand–Levitan–Marchenko integral equations, using a block version of the Levinson-type Toeplitz bordering algorithm. Numerical tests carried out by comparing calculations with known exact analytical solutions confirm the stability and second order of accuracy of the proposed algorithm. We also give an example of the algorithm application to simulate the collision of a differently polarized pair of Manakov optical vector solitons.https://www.computeroptics.ru/eng/KO/Annot/KO47-6/470602e.htmlmanakov systempolarizationdispersioninverse scattering problemalgorithm |
| spellingShingle | A.E. Chernyavsky L.L. Frumin Inverse scattering transform algorithm for the Manakov system Компьютерная оптика manakov system polarization dispersion inverse scattering problem algorithm |
| title | Inverse scattering transform algorithm for the Manakov system |
| title_full | Inverse scattering transform algorithm for the Manakov system |
| title_fullStr | Inverse scattering transform algorithm for the Manakov system |
| title_full_unstemmed | Inverse scattering transform algorithm for the Manakov system |
| title_short | Inverse scattering transform algorithm for the Manakov system |
| title_sort | inverse scattering transform algorithm for the manakov system |
| topic | manakov system polarization dispersion inverse scattering problem algorithm |
| url | https://www.computeroptics.ru/eng/KO/Annot/KO47-6/470602e.html |
| work_keys_str_mv | AT aechernyavsky inversescatteringtransformalgorithmforthemanakovsystem AT llfrumin inversescatteringtransformalgorithmforthemanakovsystem |