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
Datum:2009
1. Verfasser: Moskovchenko, E.A.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2009
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
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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].
first_indexed 2025-11-24T21:22:27Z
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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
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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