Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation
We determine all cases when there exists a meromorphic solution of the ODE vw''' + bw'' + μw' + w²/2+ A = 0. This equation describes traveling waves solutions of the Kuramoto-Sivashinsky equation. It turns out that there are no other meromorphic solutions besides those...
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| Published in: | Журнал математической физики, анализа, геометрии |
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| Date: | 2006 |
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| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/106619 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation / A. Eremenko // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 3. — С. 278-286. — Бібліогр.: 19 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-106619 |
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Eremenko, A. 2016-10-01T13:30:02Z 2016-10-01T13:30:02Z 2006 Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation / A. Eremenko // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 3. — С. 278-286. — Бібліогр.: 19 назв. — англ. 1812-9471 https://nasplib.isofts.kiev.ua/handle/123456789/106619 We determine all cases when there exists a meromorphic solution of the ODE vw''' + bw'' + μw' + w²/2+ A = 0. This equation describes traveling waves solutions of the Kuramoto-Sivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions found by Kuramoto and Kudryashov. The general method used in this paper, based on Nevanlinna theory, is applicable to nding all meromorphic solutions of a wide class of nonlinear ODE. The Author thanks Tuen Wai Ng and Robert Conte for bringing to his attention the connection between papers [4] and [19], and stimulating discussions. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Журнал математической физики, анализа, геометрии Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation |
| spellingShingle |
Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation Eremenko, A. |
| title_short |
Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation |
| title_full |
Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation |
| title_fullStr |
Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation |
| title_full_unstemmed |
Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation |
| title_sort |
meromorphic traveling wave solutions of the kuramoto-sivashinsky equation |
| author |
Eremenko, A. |
| author_facet |
Eremenko, A. |
| publishDate |
2006 |
| 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 determine all cases when there exists a meromorphic solution of the ODE vw''' + bw'' + μw' + w²/2+ A = 0. This equation describes traveling waves solutions of the Kuramoto-Sivashinsky equation. It turns out that there are no other meromorphic solutions besides those explicit solutions found by Kuramoto and Kudryashov. The general method used in this paper, based on Nevanlinna theory, is applicable to nding all meromorphic solutions of a wide class of nonlinear ODE.
|
| issn |
1812-9471 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/106619 |
| citation_txt |
Meromorphic Traveling Wave Solutions of the Kuramoto-Sivashinsky Equation / A. Eremenko // Журнал математической физики, анализа, геометрии. — 2006. — Т. 2, № 3. — С. 278-286. — Бібліогр.: 19 назв. — англ. |
| work_keys_str_mv |
AT eremenkoa meromorphictravelingwavesolutionsofthekuramotosivashinskyequation |
| first_indexed |
2025-11-29T06:54:36Z |
| last_indexed |
2025-11-29T06:54:36Z |
| _version_ |
1850854615218651136 |