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...
Збережено в:
| Опубліковано в: : | Журнал математической физики, анализа, геометрии |
|---|---|
| Дата: | 2017 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/140568 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862609490994528256 |
|---|---|
| author | Filipkovska, M.S. Kotlyarov, V.P. Melamedova, E.A. |
| author_facet | Filipkovska, M.S. Kotlyarov, V.P. Melamedova, E.A. |
| 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. |
| collection | DSpace DC |
| container_title | Журнал математической физики, анализа, геометрии |
| 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.
|
| first_indexed | 2025-11-28T20:08:41Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-140568 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1812-9471 |
| language | English |
| last_indexed | 2025-11-28T20:08:41Z |
| publishDate | 2017 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | 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 |
| 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 | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/140568 |
| work_keys_str_mv | AT filipkovskams maxwellblochequationswithoutspectralbroadeninggaugeequivalencetransformationoperatorsandmatrixriemannhilbertproblems AT kotlyarovvp maxwellblochequationswithoutspectralbroadeninggaugeequivalencetransformationoperatorsandmatrixriemannhilbertproblems AT melamedovaea maxwellblochequationswithoutspectralbroadeninggaugeequivalencetransformationoperatorsandmatrixriemannhilbertproblems |