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Journal of Nonlinear Mathematical Physics Volume 14, 2007 - Issue 3
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Original Articles

Integrability analysis of the Emden-Fowler equation

K S Govinder Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Durban, 4041, Republic of South Africa E-mail: [email protected]
&
P G L Leach Research Group in Mathematical Physics, Department of Information and Communication Systems Engineering, School of Sciences,, University of the Aegean, Karlovassi, 83 200, Greece E-mail: [email protected]@math.aegean.gr; School of Mathematical Sciences, University of KwaZulu-Natal, Durban, 4041, South Africa
Pages 443-461 | Received 06 Jan 2007, Accepted 06 Apr 2007, Published online: 21 Jan 2013
 
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Abstract

The Emden-Fowler equation of index n is studied utilising the techniques of Lie and Painlevé analysis. For general n information about the integrability of this equation is obtained. The link between these two types of analyses is explored. The special cases of n = −3, 2 are also examined. As a result of the Painlevé analysis new second-order equations possessing the Painlevé property are found.

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