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Painlevé Analysis and Similarity Reductions for the Magma Equation
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2006, том 2
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Painlevé Analysis and Similarity Reductions for the Magma Equation
Інший ID:
2000 Mathematics Subject Classification: 35C05; 35Q58; 37K10
Посилання:
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.
Підтримка:
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.
Дата:
2006
Переглядів:
771
Завантажень:
242
Анотація:
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.
