Vector breathers in the Manakov system
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Vector breathers in the Manakov system
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| Автор |
Gelash, A.
Raskovalov, A. |
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| Тематика |
BREATHERS
INTEGRABLE SYSTEMS MODULATION INSTABILITY ROGUE WAVES SOLITONS DISPERSION (WAVES) NONLINEAR EQUATIONS BREATHER DISPERSION LAW INTEGRABLE SYSTEMS MANAKOV SYSTEMS MODULATION INSTABILITIES NONLINEAR INTERACTIONS ROGUE WAVES SPACE SHIFT TWO-COMPONENT TYPE II EIGENVALUES AND EIGENFUNCTIONS |
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| Описание |
We study theoretically the nonlinear interactions of vector breathers propagating on an unstable wavefield background. As a model, we use the two-component extension of the one-dimensional focusing nonlinear Schrödinger equation—the Manakov system. With the dressing method, we generate the multibreather solutions to the Manakov model. As shown previously in [D. Kraus, G. Biondini, and G. Kovačič, Nonlinearity 28(9), 3101, (2015)], the class of vector breathers is presented by three fundamental types I, II, and III. Their interactions produce a broad family of the two-component (polarized) nonlinear wave patterns. First, we demonstrate that the type I and the types II and III correspond to two different branches of the dispersion law of the Manakov system in the presence of the unstable background. Then, we investigate the key interaction scenarios, including collisions of standing and moving breathers and resonance breather transformations. Analysis of the two-breather solution allows us to derive general formulas describing phase and space shifts acquired by breathers in mutual collisions. The found expressions enable us to describe the asymptotic states of the breather interactions and interpret the resonance fusion and decay of breathers as a limiting case of infinite space shift in the case of merging breather eigenvalues. Finally, we demonstrate that only type I breathers participate in the development of modulation instability from small-amplitude perturbations withing the superregular scenario, while the breathers of types II and III, belonging to the stable branch of the dispersion law, are not involved in this process. © 2023 Wiley Periodicals LLC.
Russian Foundation for Basic Research, РФФИ: 19‐31‐60028; Ministry of Education and Science of the Russian Federation, Minobrnauka: AAAA-A18-118020190095-4; Russian Science Foundation, RSF: 19‐72‐30028 The main part of the work was supported by the Russian Science Foundation (grant no. 19‐72‐30028). The work of A.G. on Section 6 and Appendix Section A.2 was supported by RFBR grant no. 19‐31‐60028. The work of A.R. on Appendix Sections A.1 and A.4 was performed in the framework of the state assignment of the Russian Ministry of Science and Education “Quantum” No. AAAA‐A18‐118020190095‐4. The main part of the work was supported by the Russian Science Foundation (grant no. 19-72-30028). The work of A.G. on Section 6 and Appendix Section A.2 was supported by RFBR grant no. 19-31-60028. The work of A.R. on Appendix Sections A.1 and A.4 was performed in the framework of the state assignment of the Russian Ministry of Science and Education “Quantum” No. AAAA-A18-118020190095-4. The authors thank participants of Prof. V.E. Zakharov's seminar “Nonlinear Waves” and, especially, Prof. E.A. Kuznetsov for fruitful discussions. |
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| Дата |
2024-04-05T16:38:52Z
2024-04-05T16:38:52Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/submittedVersion |
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| Идентификатор |
Gelash, A & Raskovalov, A 2023, 'Vector breathers in the Manakov system', Studies in Applied Mathematics, Том. 150, № 3, стр. 841-882. https://doi.org/10.1111/sapm.12558
Gelash, A., & Raskovalov, A. (2023). Vector breathers in the Manakov system. Studies in Applied Mathematics, 150(3), 841-882. https://doi.org/10.1111/sapm.12558 0022-2526 Final All Open Access, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85147036900&doi=10.1111%2fsapm.12558&partnerID=40&md5=f89afb08d56cf1c412745d0641bb66c8 https://arxiv.org/pdf/2211.07014 http://elar.urfu.ru/handle/10995/131103 10.1111/sapm.12558 85147036900 000916440600001 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
John Wiley and Sons Inc
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| Источник |
Studies in Applied Mathematics
Studies in Applied Mathematics |
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