Talbot Effect for the Manakov System on the Torus
In this paper, the Talbot effect for the multi-component linear and nonlinear systems of the dispersive evolution equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles is investigated. Firstly, for a class of two-component linear systems satisfyin...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212251 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Talbot Effect for the Manakov System on the Torus. Zihan Yin, Jing Kang, Xiaochuan Liu and Changzheng Qu. SIGMA 20 (2024), 056, 26 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862665767448739840 |
|---|---|
| author | Yin, Zihan Kang, Jing Liu, Xiaochuan Qu, Changzheng |
| author_facet | Yin, Zihan Kang, Jing Liu, Xiaochuan Qu, Changzheng |
| citation_txt | Talbot Effect for the Manakov System on the Torus. Zihan Yin, Jing Kang, Xiaochuan Liu and Changzheng Qu. SIGMA 20 (2024), 056, 26 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | In this paper, the Talbot effect for the multi-component linear and nonlinear systems of the dispersive evolution equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles is investigated. Firstly, for a class of two-component linear systems satisfying the dispersive quantization conditions, we discuss the fractal solutions at irrational times. Next, the investigation of the nonlinear regime is extended, and we prove that, for the concrete example of the Manakov system, the solutions of the corresponding periodic initial-boundary value problem subject to initial data of bounded variation are continuous but nowhere differentiable fractal-like curves with Minkowski dimension 3/2 at irrational times. Finally, numerical experiments for the periodic initial-boundary value problem of the Manakov system are used to justify how such effects persist into the multi-component nonlinear regime. Furthermore, it is shown in the nonlinear multi-component regime that the interplay of different components may induce subtly different qualitative profiles between the jump discontinuities, especially in the case that two nonlinearly coupled components start with different initial profiles.
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| first_indexed | 2026-03-16T09:09:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212251 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-16T09:09:55Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Yin, Zihan Kang, Jing Liu, Xiaochuan Qu, Changzheng 2026-02-03T07:54:02Z 2024 Talbot Effect for the Manakov System on the Torus. Zihan Yin, Jing Kang, Xiaochuan Liu and Changzheng Qu. SIGMA 20 (2024), 056, 26 pages 1815-0659 2020 Mathematics Subject Classification: 37K55; 35Q51 arXiv:2311.07195 https://nasplib.isofts.kiev.ua/handle/123456789/212251 https://doi.org/10.3842/SIGMA.2024.056 In this paper, the Talbot effect for the multi-component linear and nonlinear systems of the dispersive evolution equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profiles is investigated. Firstly, for a class of two-component linear systems satisfying the dispersive quantization conditions, we discuss the fractal solutions at irrational times. Next, the investigation of the nonlinear regime is extended, and we prove that, for the concrete example of the Manakov system, the solutions of the corresponding periodic initial-boundary value problem subject to initial data of bounded variation are continuous but nowhere differentiable fractal-like curves with Minkowski dimension 3/2 at irrational times. Finally, numerical experiments for the periodic initial-boundary value problem of the Manakov system are used to justify how such effects persist into the multi-component nonlinear regime. Furthermore, it is shown in the nonlinear multi-component regime that the interplay of different components may induce subtly different qualitative profiles between the jump discontinuities, especially in the case that two nonlinearly coupled components start with different initial profiles. The authors would like to thank the referees for their valuable suggestions and comments. Yin’s research was supported by Northwest University Youbo Funds 2024006. Kang’s research was supported by NSFC under Grant 12371252 and Basic Science Program of Shaanxi Province (Grant-2019JC-28). Liu’s research was supported by NSFC under Grant 12271424. Qu’s research was supported by NSFC under Grant 11971251 and Grant 11631007. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Talbot Effect for the Manakov System on the Torus Article published earlier |
| spellingShingle | Talbot Effect for the Manakov System on the Torus Yin, Zihan Kang, Jing Liu, Xiaochuan Qu, Changzheng |
| title | Talbot Effect for the Manakov System on the Torus |
| title_full | Talbot Effect for the Manakov System on the Torus |
| title_fullStr | Talbot Effect for the Manakov System on the Torus |
| title_full_unstemmed | Talbot Effect for the Manakov System on the Torus |
| title_short | Talbot Effect for the Manakov System on the Torus |
| title_sort | talbot effect for the manakov system on the torus |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212251 |
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