On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves

We discuss an asymptotical behavior of the rarefaction wave for the KdV equation in the region behind the wave front. The first and the second terms of the asymptotical expansion for such a solution with respect to large time were derived without detailed analysis in [1]. In the present work, we cor...

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Veröffentlicht in:Журнал математической физики, анализа, геометрии
Datum:2017
Hauptverfasser: Andreiev, K., Egorova, I.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2017
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/140579
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Zitieren:On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves / K. Andreiev, I. Egorova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 4. — С. 325-343. — Бібліогр.: 15 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Andreiev, K.
Egorova, I.
author_facet Andreiev, K.
Egorova, I.
citation_txt On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves / K. Andreiev, I. Egorova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 4. — С. 325-343. — Бібліогр.: 15 назв. — англ.
collection DSpace DC
container_title Журнал математической физики, анализа, геометрии
description We discuss an asymptotical behavior of the rarefaction wave for the KdV equation in the region behind the wave front. The first and the second terms of the asymptotical expansion for such a solution with respect to large time were derived without detailed analysis in [1]. In the present work, we correct the formula for the second term by investigating the corresponding parametrix problem. We also study an in uence of the resonance on the asymptotical behavior of the solution.
first_indexed 2025-12-07T18:54:05Z
format Article
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id nasplib_isofts_kiev_ua-123456789-140579
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1812-9471
language English
last_indexed 2025-12-07T18:54:05Z
publishDate 2017
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
record_format dspace
spelling Andreiev, K.
Egorova, I.
2018-07-10T20:19:55Z
2018-07-10T20:19:55Z
2017
On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves / K. Andreiev, I. Egorova // Журнал математической физики, анализа, геометрии. — 2017. — Т. 13, № 4. — С. 325-343. — Бібліогр.: 15 назв. — англ.
1812-9471
DOI: doi.org/10.15407/mag13.04.325
Mathematics Subject Classification 2000: 37K40, 35Q53, 35Q15
https://nasplib.isofts.kiev.ua/handle/123456789/140579
We discuss an asymptotical behavior of the rarefaction wave for the KdV equation in the region behind the wave front. The first and the second terms of the asymptotical expansion for such a solution with respect to large time were derived without detailed analysis in [1]. In the present work, we correct the formula for the second term by investigating the corresponding parametrix problem. We also study an in uence of the resonance on the asymptotical behavior of the solution.
en
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
Журнал математической физики, анализа, геометрии
On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves
Article
published earlier
spellingShingle On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves
Andreiev, K.
Egorova, I.
title On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves
title_full On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves
title_fullStr On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves
title_full_unstemmed On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves
title_short On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves
title_sort on the long-time asymptotics for the korteweg-de vries equation with steplike initial data associated with rarefaction waves
url https://nasplib.isofts.kiev.ua/handle/123456789/140579
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