Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening
The Maxwell-Bloch equations have been intensively studied by many authors. The main results are based on the inverse scattering transform and the Marchenko integral equations. However this method is not acceptable for mixed problems. In the paper, we develop a method allowing to linearize mixed prob...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2014
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| Schriftenreihe: | Журнал математической физики, анализа, геометрии |
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| Zitieren: | Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening / V.P. Kotlyarov, E.A. Moskovchenko // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 3. — С. 328-349. — Бібліогр.: 24 назв. — англ. |
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irk-123456789-1068022016-10-06T03:02:26Z Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening Kotlyarov, V.P. Moskovchenko, E.A. The Maxwell-Bloch equations have been intensively studied by many authors. The main results are based on the inverse scattering transform and the Marchenko integral equations. However this method is not acceptable for mixed problems. In the paper, we develop a method allowing to linearize mixed problems. It is based on simultaneous spectral analysis of both Lax equations and the matrix Riemann{Hilbert problems. We consider the case of infinitely narrow spectral line, i.e., without spectrum broadening. The proposed matrix Riemann-Hilbert problem can be used for studying temporal/spatial asymptotics of the solutions of Maxwell-Bloch equations by using a nonlinear method of steepest descent. Уравнения Максвелла-Блоха интенсивно изучаются многими авторами. Основные результаты базируются на методе обратной задачи с использованием интегральных уравнений Марченко. Однако такой метод оказался неприемлемым для смешанных задач. В данной работе мы развиваем метод, позволяющий линеаризовать смешанные задачи. Он основан на одновременном спектральном анализе обоих уравнений Лакса и матричных задачах Римана-Гильберта. Мы рассматриваем случай бесконечно узкой спектральной линии, т.е. без уширения спектра. Предлагаемые матричные задачи Римана-Гильберта будут полезны для изучения временных/пространственных асимптотик решений уравнений Максвелла-Блоха, используя нелинейный метод наискорейшего спуска. 2014 Article Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening / V.P. Kotlyarov, E.A. Moskovchenko // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 3. — С. 328-349. — Бібліогр.: 24 назв. — англ. 1812-9471 http://dspace.nbuv.gov.ua/handle/123456789/106802 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 |
The Maxwell-Bloch equations have been intensively studied by many authors. The main results are based on the inverse scattering transform and the Marchenko integral equations. However this method is not acceptable for mixed problems. In the paper, we develop a method allowing to linearize mixed problems. It is based on simultaneous spectral analysis of both Lax equations and the matrix Riemann{Hilbert problems. We consider the case of infinitely narrow spectral line, i.e., without spectrum broadening. The proposed matrix Riemann-Hilbert problem can be used for studying temporal/spatial asymptotics of the solutions of Maxwell-Bloch equations by using a nonlinear method of steepest descent. |
| format |
Article |
| author |
Kotlyarov, V.P. Moskovchenko, E.A. |
| spellingShingle |
Kotlyarov, V.P. Moskovchenko, E.A. Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening Журнал математической физики, анализа, геометрии |
| author_facet |
Kotlyarov, V.P. Moskovchenko, E.A. |
| author_sort |
Kotlyarov, V.P. |
| title |
Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening |
| title_short |
Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening |
| title_full |
Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening |
| title_fullStr |
Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening |
| title_full_unstemmed |
Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening |
| title_sort |
matrix riemann-hilbert problems and maxwell-bloch equations without spectral broadening |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/106802 |
| citation_txt |
Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening / V.P. Kotlyarov, E.A. Moskovchenko // Журнал математической физики, анализа, геометрии. — 2014. — Т. 10, № 3. — С. 328-349. — Бібліогр.: 24 назв. — англ. |
| series |
Журнал математической физики, анализа, геометрии |
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2025-07-07T19:03:18Z |
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2025-07-07T19:03:18Z |
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