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
Date:2006
Main Author: Eremenko, A.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2006
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
record_format dspace
spelling 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
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