Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering
We consider the initial-boundary value (IBV) problem for nonlinear equations related to the integrable model of the stimulated Raman scattering in the quarter xt-plane with vanishing at infinity initial conditions and single-frequency periodic boundary data. We propose a matrix Riemann-Hilbert probl...
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| Veröffentlicht in: | Журнал математической физики, анализа, геометрии |
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| Datum: | 2009 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2009
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/106534 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering / E.A. Moskovchenko // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 1. — С. 82-103. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862543053304102912 |
|---|---|
| author | Moskovchenko, E.A. |
| author_facet | Moskovchenko, E.A. |
| citation_txt | Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering / E.A. Moskovchenko // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 1. — С. 82-103. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| description | We consider the initial-boundary value (IBV) problem for nonlinear equations related to the integrable model of the stimulated Raman scattering in the quarter xt-plane with vanishing at infinity initial conditions and single-frequency periodic boundary data. We propose a matrix Riemann-Hilbert problem, which provides the existence of the solution of the IBV problem for all t and allows us to obtain an explicit formula for the asymptotics of the solution, using the steepest descent method for the oscillatory matrix RH problem introduced by P. Deift and X. Zhou [6].
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| first_indexed | 2025-11-24T21:22:27Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-106534 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-11-24T21:22:27Z |
| publishDate | 2009 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Moskovchenko, E.A. 2016-09-30T06:19:47Z 2016-09-30T06:19:47Z 2009 Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering / E.A. Moskovchenko // Журнал математической физики, анализа, геометрии. — 2009. — Т. 5, № 1. — С. 82-103. — Бібліогр.: 14 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106534 We consider the initial-boundary value (IBV) problem for nonlinear equations related to the integrable model of the stimulated Raman scattering in the quarter xt-plane with vanishing at infinity initial conditions and single-frequency periodic boundary data. We propose a matrix Riemann-Hilbert problem, which provides the existence of the solution of the IBV problem for all t and allows us to obtain an explicit formula for the asymptotics of the solution, using the steepest descent method for the oscillatory matrix RH problem introduced by P. Deift and X. Zhou [6]. The author thanks V.P. Kotlyarov and D.G. Shepelsky for helpful discussions, comments and remarks. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering Article published earlier |
| spellingShingle | Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering Moskovchenko, E.A. |
| title | Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering |
| title_full | Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering |
| title_fullStr | Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering |
| title_full_unstemmed | Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering |
| title_short | Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering |
| title_sort | simple periodic boundary data and riemann-hilbert problem for integrable model of the stimulated raman scattering |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/106534 |
| work_keys_str_mv | AT moskovchenkoea simpleperiodicboundarydataandriemannhilbertproblemforintegrablemodelofthestimulatedramanscattering |