Painlevé Analysis and Similarity Reductions for the Magma Equation
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Painlevé Analysis and Similarity Reductions for the Magma Equation
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| Creator |
Harris, S.E.
Clarkson, P.A. |
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| 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.
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| Date |
2019-02-07T13:13:12Z
2019-02-07T13:13:12Z 2006 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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