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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 068, 17 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.068
(Mi sigma96)
 

This article is cited in 12 scientific papers (total in 12 papers)

Painlevé Analysis and Similarity Reductions for the Magma Equation

Shirley E.  Harrisa, Peter A. Clarksonb

a Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford, OX1 3LB, UK
b Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF, UK
References:
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 $m=\frac12$, $n=-\frac12$, it is a real, generalized, pumped Maxwell–Bloch equation.
Keywords: Painlevé analysis; similarity reductions; magma equation.
Received: September 27, 2006; Published online October 5, 2006
Bibliographic databases:
Document Type: Article
MSC: 35C05; 35Q58; 37K10
Language: English
Citation: Shirley E. Harris, Peter A. Clarkson, “Painlevé Analysis and Similarity Reductions for the Magma Equation”, SIGMA, 2 (2006), 068, 17 pp.
Citation in format AMSBIB
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\by Shirley E.~ Harris, Peter A.~Clarkson
\paper Painlev\'e Analysis and Similarity Reductions for the Magma Equation
\jour SIGMA
\yr 2006
\vol 2
\papernumber 068
\totalpages 17
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  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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