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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| Veröffentlicht in: | Журнал математической физики, анализа, геометрии |
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| Datum: | 2006 |
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| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2006
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/106619 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
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| ISSN: | 1812-9471 |