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INTEGRATION OF SYSTEMS OF FIRST-ORDER EQUATIONS ADMITTING NONLINEAR SUPERPOSITION
Responsible organisation
2009 (English)Conference paper, Published paper (Refereed) Published
Abstract [en]

Systems of two nonlinear ordinary differential equations of the first order admitting nonlinear superpositions are investigated using Lie's enumeration of groups on the plane. It is shown that the systems associated with two-dimensional Vessiot-Guldberg-Lie algebras can be integrated by quadrature upon introducing Lie's canonical variables. The knowledge of a symmetry group of a system in question is not needed in this approach. The systems associated with three-dimensional Vessiot-Guldberg-Lie algebras are classified into 13 standard forms 10 of which are integrable by quadratures and three are reduced to Riccati equations.

Place, publisher, year, edition, pages
Durban: ATLANTIS PRESS , 2009.
Keyword [en]
Nonlinear superposition, Vessiot-Guldberg-Lie algebras, standard forms of Lie algebras, canonical variables
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-7909DOI: 10.1142/S1402925109000364Local ID: oai:bth.se:forskinfo233B689145EABA5BC12576AC003B5AD6OAI: oai:DiVA.org:bth-7909DiVA: diva2:835582
Conference
Workshop on Nonlinear Differential Equations
Available from: 2012-09-18 Created: 2010-01-15 Last updated: 2015-06-30Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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Output format
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