First integrals and parametric solutions for equations integrable through Lie symmetries

J. Nonlinear Math. Phys. 8 (2001), no. 2, 211-216 We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The co...

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Hauptverfasser:	Géronimi, Claude, Leach, Peter, Feix, Marc R
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Sprache:	eng
Schlagworte:	Physics - Exactly Solvable and Integrable Systems
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creator	Géronimi, Claude Leach, Peter Feix, Marc R
description	J. Nonlinear Math. Phys. 8 (2001), no. 2, 211-216 We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computation of first integrals gives in the most general case, the parametric form of the general solution. For some polynomial functions we obtain a time parametrisation quadrature which can be solved in terms of ``known'' functions.
doi_str_mv	10.48550/arxiv.nlin/0104074
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Phys. 8 (2001), no. 2, 211-216 We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computation of first integrals gives in the most general case, the parametric form of the general solution. For some polynomial functions we obtain a time parametrisation quadrature which can be solved in terms of ``known'' functions.</description><identifier>DOI: 10.48550/arxiv.nlin/0104074</identifier><language>eng</language><subject>Physics - Exactly Solvable and Integrable Systems</subject><creationdate>2001-03</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/nlin/0104074$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.nlin/0104074$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.2991/jnmp.2001.8.2.4$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Géronimi, Claude</creatorcontrib><creatorcontrib>Leach, Peter</creatorcontrib><creatorcontrib>Feix, Marc R</creatorcontrib><title>First integrals and parametric solutions for equations integrable through Lie symmetries</title><description>J. Nonlinear Math. Phys. 8 (2001), no. 2, 211-216 We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computation of first integrals gives in the most general case, the parametric form of the general solution. 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Nonlinear Math. Phys. 8 (2001), no. 2, 211-216 We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity symmetries. The computation of first integrals gives in the most general case, the parametric form of the general solution. For some polynomial functions we obtain a time parametrisation quadrature which can be solved in terms of ``known'' functions.</abstract><doi>10.48550/arxiv.nlin/0104074</doi><oa>free_for_read</oa></addata></record>
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title	First integrals and parametric solutions for equations integrable through Lie symmetries
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