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 |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
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| Online Zugang: | 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 |
| 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| _version_ | 1862725714988498944 |
|---|---|
| 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.
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| first_indexed | 2025-12-07T18:54:05Z |
| format | Article |
| fulltext | |
| 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 |
| work_keys_str_mv | AT andreievk onthelongtimeasymptoticsforthekortewegdevriesequationwithsteplikeinitialdataassociatedwithrarefactionwaves AT egorovai onthelongtimeasymptoticsforthekortewegdevriesequationwithsteplikeinitialdataassociatedwithrarefactionwaves |