Painlevé Analysis and Similarity Reductions for the Magma Equation

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2006
• Main Authors: Harris, S.E., Clarkson, P.A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2006
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146099
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: 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.

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...