Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
Painlevé Analysis and Similarity Reductions for the Magma Equation
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
| dc.contributor.author | Harris, S.E. | |
| dc.contributor.author | Clarkson, P.A. | |
| dc.date.accessioned | 2019-02-07T13:13:12Z | |
| dc.date.available | 2019-02-07T13:13:12Z | |
| dc.date.issued | 2006 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2000 Mathematics Subject Classification: 35C05; 35Q58; 37K10 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/146099 | |
| dc.description.abstract | 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. | uk_UA |
| dc.description.sponsorship | It is a pleasure to thank Elizabeth Mansfield and Andrew Pickering for their helpful comments and discussions. SEH gratefully acknowledges the support of a Darby Fellowship at Lincoln College, Oxford and a Grace Chisholm Young Fellowship from the London Mathematical Society for the period in which this research was carried out. PAC thanks the Isaac Newton Institute, Cambridge for their hospitality during his visit as part of the programme on “Painlev´e Equations and Monodromy Problems” when this paper was completed. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | Painlevé Analysis and Similarity Reductions for the Magma Equation | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
