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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| Дата: | 2007 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
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dspace |
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irk-123456789-1473842019-02-15T01:24:58Z Do All Integrable Evolution Equations Have the Painlevé Property? Tamizhmani, K.M. Grammaticos, B. Ramani, A. 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). 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147384 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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). |
| format |
Article |
| author |
Tamizhmani, K.M. Grammaticos, B. Ramani, A. |
| spellingShingle |
Tamizhmani, K.M. Grammaticos, B. Ramani, A. Do All Integrable Evolution Equations Have the Painlevé Property? Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Tamizhmani, K.M. Grammaticos, B. Ramani, A. |
| author_sort |
Tamizhmani, K.M. |
| title |
Do All Integrable Evolution Equations Have the Painlevé Property? |
| title_short |
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_sort |
do all integrable evolution equations have the painlevé property? |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147384 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:27:11Z |
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2023-05-20T17:27:11Z |
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