Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems
A mixed initial-boundary value problem for nonlinear Maxwell{Bloch (MB) equations without spectral broadening is studied by using the inverse scattering transform in the form of the matrix Riemann{Hilbert (RH) problem. We use transformation operators whose existence is closely related with the Gours...
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| Опубліковано в: : | Журнал математической физики, анализа, геометрии |
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| Дата: | 2017 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/140568 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems / M.S. Filipkovska, V.P. Kotlyarov, E.A. Melamedova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 2. — С. 119-153. — Бібліогр.: 31 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-140568 |
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Filipkovska, M.S. Kotlyarov, V.P. Melamedova, E.A. 2018-07-10T18:29:37Z 2018-07-10T18:29:37Z 2017 Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems / M.S. Filipkovska, V.P. Kotlyarov, E.A. Melamedova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 2. — С. 119-153. — Бібліогр.: 31 назв. — англ. 1812-9471 DOI: doi.org/10.15407/mag13.02.119 Mathematics Subject Classification 2000: 34L25, 34M50, 35F31, 35Q15, 35Q51 https://nasplib.isofts.kiev.ua/handle/123456789/140568 A mixed initial-boundary value problem for nonlinear Maxwell{Bloch (MB) equations without spectral broadening is studied by using the inverse scattering transform in the form of the matrix Riemann{Hilbert (RH) problem. We use transformation operators whose existence is closely related with the Goursat problems with nontrivial characteristics. We also use a gauge transformation which allows us to obtain Goursat problems of the canonical type with rectilinear characteristics, the solvability of which is known. The transformation operators and a gauge transformation are used to obtain the Jost type solutions of the Ablowitz-Kaup-Newel-Segur equations with well-controlled asymptotic behavior by the spectral parameter near singular points. A well posed regular matrix RH problem in the sense of the feasibility of the Schwartz symmetry principle is obtained. The matrix RH problem generates the solution of the mixed problem for MB equations. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems |
| spellingShingle |
Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems Filipkovska, M.S. Kotlyarov, V.P. Melamedova, E.A. |
| title_short |
Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems |
| title_full |
Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems |
| title_fullStr |
Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems |
| title_full_unstemmed |
Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems |
| title_sort |
maxwell-bloch equations without spectral broadening: gauge equivalence, transformation operators and matrix riemann-hilbert problems |
| author |
Filipkovska, M.S. Kotlyarov, V.P. Melamedova, E.A. |
| author_facet |
Filipkovska, M.S. Kotlyarov, V.P. Melamedova, E.A. |
| publishDate |
2017 |
| language |
English |
| container_title |
Журнал математической физики, анализа, геометрии |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
A mixed initial-boundary value problem for nonlinear Maxwell{Bloch (MB) equations without spectral broadening is studied by using the inverse scattering transform in the form of the matrix Riemann{Hilbert (RH) problem. We use transformation operators whose existence is closely related with the Goursat problems with nontrivial characteristics. We also use a gauge transformation which allows us to obtain Goursat problems of the canonical type with rectilinear characteristics, the solvability of which is known. The transformation operators and a gauge transformation are used to obtain the Jost type solutions of the Ablowitz-Kaup-Newel-Segur equations with well-controlled asymptotic behavior by the spectral parameter near singular points. A well posed regular matrix RH problem in the sense of the feasibility of the Schwartz symmetry principle is obtained. The matrix RH problem generates the solution of the mixed problem for MB equations.
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| issn |
1812-9471 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/140568 |
| citation_txt |
Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems / M.S. Filipkovska, V.P. Kotlyarov, E.A. Melamedova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 2. — С. 119-153. — Бібліогр.: 31 назв. — англ. |
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2025-11-28T20:08:41Z |
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2025-11-28T20:08:41Z |
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