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INTEGRATION OF SYSTEMS OF FIRST-ORDER EQUATIONS ADMITTING NONLINEAR SUPERPOSITION
Ansvarig organisation
2009 (Engelska)Konferensbidrag, Publicerat paper (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Durban: ATLANTIS PRESS , 2009.
Nyckelord [en]
Nonlinear superposition, Vessiot-Guldberg-Lie algebras, standard forms of Lie algebras, canonical variables
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:bth-7909DOI: 10.1142/S1402925109000364Lokalt ID: oai:bth.se:forskinfo233B689145EABA5BC12576AC003B5AD6OAI: oai:DiVA.org:bth-7909DiVA, id: diva2:835582
Konferens
Workshop on Nonlinear Differential Equations
Tillgänglig från: 2012-09-18 Skapad: 2010-01-15 Senast uppdaterad: 2015-06-30Bibliografiskt granskad

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