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Invariant solutions as internal singularities of nonlinear differential equations and their use for qualitative analysis of implicit and numerical solutions
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2009 (English)In: Communications in nonlinear science & numerical simulation, ISSN 1007-5704, Vol. 14, no 9-10, 3537-3547 p.Article in journal (Refereed) Published
Abstract [en]

Lie group analysis of nonlinear differential equations reveals existence of singularities provided by invariant solutions and invisible from the form of the equation in question. We call them internal singularities in contrast with external singularities manifested by the form of the equation. It is illustrated by way of examples that internal singularities are useful for analyzing a behaviour of solutions of nonlinear differential equations near external singularities.

Place, publisher, year, edition, pages
Elsevier Science , 2009. Vol. 14, no 9-10, 3537-3547 p.
Keyword [en]
Nonlinear equations, Lie group analysis, Internal and external singularities
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-7936DOI: 10.1016/j.cnsns.2009.01.025ISI: 000265712200007Local ID: oai:bth.se:forskinfo3D1EC3D5B7C211EDC125766A002C121DOAI: oai:DiVA.org:bth-7936DiVA: diva2:835613
Available from: 2012-09-18 Created: 2009-11-10 Last updated: 2015-06-30Bibliographically approved

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