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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| Дата: | 2009 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2009
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| Назва видання: | Журнал математической физики, анализа, геометрии |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/106534 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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dspace |
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irk-123456789-1065342016-10-01T03:01:47Z Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering Moskovchenko, E.A. 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]. 2009 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/106534 en Журнал математической физики, анализа, геометрии Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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]. |
| format |
Article |
| author |
Moskovchenko, E.A. |
| spellingShingle |
Moskovchenko, E.A. Simple Periodic Boundary Data and Riemann-Hilbert Problem for Integrable Model of the Stimulated Raman Scattering Журнал математической физики, анализа, геометрии |
| author_facet |
Moskovchenko, E.A. |
| author_sort |
Moskovchenko, E.A. |
| title |
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_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_sort |
simple periodic boundary data and riemann-hilbert problem for integrable model of the stimulated raman scattering |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2009 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106534 |
| 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. |
| series |
Журнал математической физики, анализа, геометрии |
| work_keys_str_mv |
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2023-10-18T20:13:09Z |
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2023-10-18T20:13:09Z |
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