Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis
An initial-boundary value problem for a model of stimulated Raman scattering was considered in [Moskovchenko E.A., Kotlyarov V.P., J. Phys. A: Math. Theor. 43 (2010), 055205, 31 pages]. The authors showed that in the long-time range t→+∞, the x>0, t>0 quarter plane is divided into 3 regions wi...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2018 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2018
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/209838 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis / R.R. Aydagulov, A.A. Minakov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ. |
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Aydagulov, R.R. Minakov, A.A. 2025-11-27T14:46:57Z 2018 Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis / R.R. Aydagulov, A.A. Minakov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37K15; 35Q51; 37K40 arXiv: 1805.05153 https://nasplib.isofts.kiev.ua/handle/123456789/209838 https://doi.org/10.3842/SIGMA.2018.119 An initial-boundary value problem for a model of stimulated Raman scattering was considered in [Moskovchenko E.A., Kotlyarov V.P., J. Phys. A: Math. Theor. 43 (2010), 055205, 31 pages]. The authors showed that in the long-time range t→+∞, the x>0, t>0 quarter plane is divided into 3 regions with qualitatively different asymptotic behavior of the solution: a region of a finite amplitude plane wave, a modulated elliptic wave region, and a vanishing dispersive wave region. The asymptotics in the modulated elliptic region were studied under an implicit assumption of the solvability of the corresponding Whitham-type equations. Here, we establish the existence of these parameters and thus justify the results by Moskovchenko and Kotlyarov. A.M. would like to thank Vladimir Kotlyarov for useful discussions, and Koen van den Dungen and Rémy Rodiac for careful reading of a version of this manuscript and for giving valuable comments and suggestions. Also, the authors thank the anonymous referees for careful reading of the manuscript and their comments and suggestions. Last, but not least, A.M. is also grateful to Questura di Trieste, in whose queue a part of this work was done. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis |
| spellingShingle |
Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis Aydagulov, R.R. Minakov, A.A. |
| title_short |
Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis |
| title_full |
Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis |
| title_fullStr |
Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis |
| title_full_unstemmed |
Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis |
| title_sort |
initial-boundary value problem for stimulated raman scattering model: solvability of whitham type system of equations arising in long-time asymptotic analysis |
| author |
Aydagulov, R.R. Minakov, A.A. |
| author_facet |
Aydagulov, R.R. Minakov, A.A. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
An initial-boundary value problem for a model of stimulated Raman scattering was considered in [Moskovchenko E.A., Kotlyarov V.P., J. Phys. A: Math. Theor. 43 (2010), 055205, 31 pages]. The authors showed that in the long-time range t→+∞, the x>0, t>0 quarter plane is divided into 3 regions with qualitatively different asymptotic behavior of the solution: a region of a finite amplitude plane wave, a modulated elliptic wave region, and a vanishing dispersive wave region. The asymptotics in the modulated elliptic region were studied under an implicit assumption of the solvability of the corresponding Whitham-type equations. Here, we establish the existence of these parameters and thus justify the results by Moskovchenko and Kotlyarov.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209838 |
| citation_txt |
Initial-Boundary Value Problem for Stimulated Raman Scattering Model: Solvability of Whitham Type System of Equations Arising in Long-Time Asymptotic Analysis / R.R. Aydagulov, A.A. Minakov // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ. |
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