Symmetry analysis of the bidimensional Lane-Emden systems
type: Item
instance of: scholarly article
title: Symmetry analysis of the bidimensional Lane-Emden systems
zbMATH Open document ID: 1298.35009
published in: Journal of Mathematical Analysis and Applications
publication date: 2012-02-27T00:00:00Z
review text: The paper addresses the system of Lane-Emden equations in two-dimensional space, which appear in astrophysics as models for the description of the intrinsic state of stars: \[ \Delta u + |v|^{q-1}v =0, \quad \Delta v + |u|^{q-1}u =0, \] where \(p\) and \(q\) are real constants (positive or negative). The paper reports on results of the analysis of the Noether symmetries and related conservation laws of this system. In particular, the dilation symmetry exists only along the curve \(p+q=-2\) (for \(p\neq-1\) and \(q\neq -1\)). This curve is simulataneously a critical one which separates the regions of existence and nonexistence of positive solutions to the system.
reviewed by: B. A. Malomed
Mathematics Subject Classification ID: 35B06
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 85A15
zbMATH DE Number: 6009635
zbMATH Keywords: Noether symmetries
zbMATH Keywords: group-symmetry analysis
zbMATH Keywords: Lane-Emden system
zbMATH Keywords: conservation laws
zbMATH Keywords: intrinsic state of stars
author: Yuri Bozhkov
author: Igor Leite Freire
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.11.024
OpenAlex ID: W1981516410
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DOI: 10.1016/J.JMAA.2011.11.024
description: scientific article; zbMATH DE number 6009635