Do All Integrable Evolution Equations Have the Painlevé Property?
We examine whether the Painlevé property is necessary for the integrability of partial differential equations (PDEs). We show that in analogy to what happens in the case of ordinary differential equations (ODEs) there exists a class of PDEs, integrable through linearisation, which do not possess the...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2007 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2007
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/147384 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Do All Integrable Evolution Equations Have the Painlevé Property? / K.M. Tamizhmani, B. Grammaticos, A. Ramani // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 17 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725510470041600 |
|---|---|
| author | Tamizhmani, K.M. Grammaticos, B. Ramani, A. |
| author_facet | Tamizhmani, K.M. Grammaticos, B. Ramani, A. |
| citation_txt | Do All Integrable Evolution Equations Have the Painlevé Property? / K.M. Tamizhmani, B. Grammaticos, A. Ramani // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 17 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We examine whether the Painlevé property is necessary for the integrability of partial differential equations (PDEs). We show that in analogy to what happens in the case of ordinary differential equations (ODEs) there exists a class of PDEs, integrable through linearisation, which do not possess the Painlevé property. The same question is addressed in a discrete setting where we show that there exist linearisable lattice equations which do not possess the singularity confinement property (again in analogy to the one-dimensional case).
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| first_indexed | 2025-12-07T18:52:42Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147384 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:52:42Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Tamizhmani, K.M. Grammaticos, B. Ramani, A. 2019-02-14T14:57:07Z 2019-02-14T14:57:07Z 2007 Do All Integrable Evolution Equations Have the Painlevé Property? / K.M. Tamizhmani, B. Grammaticos, A. Ramani // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 17 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 34A99; 35A21; 39A12 https://nasplib.isofts.kiev.ua/handle/123456789/147384 We examine whether the Painlevé property is necessary for the integrability of partial differential equations (PDEs). We show that in analogy to what happens in the case of ordinary differential equations (ODEs) there exists a class of PDEs, integrable through linearisation, which do not possess the Painlevé property. The same question is addressed in a discrete setting where we show that there exist linearisable lattice equations which do not possess the singularity confinement property (again in analogy to the one-dimensional case). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Do All Integrable Evolution Equations Have the Painlevé Property? Article published earlier |
| spellingShingle | Do All Integrable Evolution Equations Have the Painlevé Property? Tamizhmani, K.M. Grammaticos, B. Ramani, A. |
| title | Do All Integrable Evolution Equations Have the Painlevé Property? |
| title_full | Do All Integrable Evolution Equations Have the Painlevé Property? |
| title_fullStr | Do All Integrable Evolution Equations Have the Painlevé Property? |
| title_full_unstemmed | Do All Integrable Evolution Equations Have the Painlevé Property? |
| title_short | Do All Integrable Evolution Equations Have the Painlevé Property? |
| title_sort | do all integrable evolution equations have the painlevé property? |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147384 |
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