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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| 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/123456789/140579 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-140579 |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data Associated with Rarefaction Waves |
| 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_short |
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_sort |
on the long-time asymptotics for the korteweg-de vries equation with steplike initial data associated with rarefaction waves |
| author |
Andreiev, K. Egorova, I. |
| author_facet |
Andreiev, K. Egorova, I. |
| 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 |
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.
|
| issn |
1812-9471 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/140579 |
| 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. |
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2025-12-07T18:54:05Z |
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2025-12-07T18:54:05Z |
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