Painlevé Analysis and Similarity Reductions for the Magma Equation
In this paper, we examine a generalized magma equation for rational values of two parameters, m and n. Firstly, the similarity reductions are found using the Lie group method of infinitesimal transformations. The Painlevé ODE test is then applied to the travelling wave reduction, and the pairs of m...
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| Дата: | 2006 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146099 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Painlevé Analysis and Similarity Reductions for the Magma Equation / S.E. Harris, P.A. Clarkson // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 34 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1460992019-02-08T01:23:53Z Painlevé Analysis and Similarity Reductions for the Magma Equation Harris, S.E. Clarkson, P.A. In this paper, we examine a generalized magma equation for rational values of two parameters, m and n. Firstly, the similarity reductions are found using the Lie group method of infinitesimal transformations. The Painlevé ODE test is then applied to the travelling wave reduction, and the pairs of m and n which pass the test are identified. These particular pairs are further subjected to the ODE test on their other symmetry reductions. Only two cases remain which pass the ODE test for all such symmetry reductions and these are completely integrable. The case when m = 0, n = −1 is related to the Hirota-Satsuma equation and for m = ½, n = −½, it is a real, generalized, pumped Maxwell-Bloch equation. 2006 Article Painlevé Analysis and Similarity Reductions for the Magma Equation / S.E. Harris, P.A. Clarkson // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 34 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 35C05; 35Q58; 37K10 http://dspace.nbuv.gov.ua/handle/123456789/146099 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 |
In this paper, we examine a generalized magma equation for rational values of two parameters, m and n. Firstly, the similarity reductions are found using the Lie group method of infinitesimal transformations. The Painlevé ODE test is then applied to the travelling wave reduction, and the pairs of m and n which pass the test are identified. These particular pairs are further subjected to the ODE test on their other symmetry reductions. Only two cases remain which pass the ODE test for all such symmetry reductions and these are completely integrable. The case when m = 0, n = −1 is related to the Hirota-Satsuma equation and for m = ½, n = −½, it is a real, generalized, pumped Maxwell-Bloch equation. |
| format |
Article |
| author |
Harris, S.E. Clarkson, P.A. |
| spellingShingle |
Harris, S.E. Clarkson, P.A. Painlevé Analysis and Similarity Reductions for the Magma Equation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Harris, S.E. Clarkson, P.A. |
| author_sort |
Harris, S.E. |
| title |
Painlevé Analysis and Similarity Reductions for the Magma Equation |
| title_short |
Painlevé Analysis and Similarity Reductions for the Magma Equation |
| title_full |
Painlevé Analysis and Similarity Reductions for the Magma Equation |
| title_fullStr |
Painlevé Analysis and Similarity Reductions for the Magma Equation |
| title_full_unstemmed |
Painlevé Analysis and Similarity Reductions for the Magma Equation |
| title_sort |
painlevé analysis and similarity reductions for the magma equation |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146099 |
| citation_txt |
Painlevé Analysis and Similarity Reductions for the Magma Equation / S.E. Harris, P.A. Clarkson // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 34 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT harrisse painleveanalysisandsimilarityreductionsforthemagmaequation AT clarksonpa painleveanalysisandsimilarityreductionsforthemagmaequation |
| first_indexed |
2023-05-20T17:23:49Z |
| last_indexed |
2023-05-20T17:23:49Z |
| _version_ |
1796153200755081216 |