Yu. R. Romanovskii, “Computation of local symmetries of second-order ordinary differential equations by the Cartan equivalence method”, Mat. Zametki, 60:1 (1996), 75–91; Math. Notes, 60:1 (1996), 56

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Matematicheskie Zametki, 1996, Volume 60, Issue 1, Pages 75–91
DOI: https://doi.org/10.4213/mzm1805 (Mi mzm1805)

This article is cited in 10 scientific papers (total in 10 papers)

Computation of local symmetries of second-order ordinary differential equations by the Cartan equivalence method

Yu. R. Romanovskii

Program Systems Institute of RAS

Full-text PDF (241 kB) Citations (10)

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DOI: https://doi.org/10.4213/mzm1805

Abstract: The Cartan equivalence method is used to find out if a given equation has a nontrivial Lie group of point symmetries. In particular, we compute invariants that permit one to recognize equations with a three-dimensional symmetry group. An effective method to transform the Lie system (the system of partial differential equations to be satisfied by the infinitesimal point symmetries) into a formally integrable form is given. For equations with a three-dimensional symmetry group, the formally integrable form of the Lie system is found explicitly.

Received: 09.04.1992
Revised: 05.03.1996

English version:
Mathematical Notes, 1996, Volume 60, Issue 1, Pages 56–67
DOI: https://doi.org/10.1007/BF02308880

Bibliographic databases:

UDC: 517

Language: Russian

Citation: Yu. R. Romanovskii, “Computation of local symmetries of second-order ordinary differential equations by the Cartan equivalence method”, Mat. Zametki, 60:1 (1996), 75–91; Math. Notes, 60:1 (1996), 56–67

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm1805

https://doi.org/10.4213/mzm1805

https://www.mathnet.ru/eng/mzm/v60/i1/p75

This publication is cited in the following 10 articles:

Maycol Falla Luza, Frank Loray, “Projective structures, neighborhoods of rational curves and Painlevé equations”, Mosc. Math. J., 23:1 (2023), 59–95
Gianni Manno, Jan Schumm, Andreas Vollmer, Contemporary Mathematics, 788, The Diverse World of PDEs, 2023, 193
Vera V. Kartak, “Point classification of second order ODEs and its application to Painlevé equations”, JNMP, 20:Supplement 1 (2021), 110
Manno G., Vollmer A., “Normal Forms of Two-Dimensional Metrics Admitting Exactly One Essential Projective Vector Field”, J. Math. Pures Appl., 135 (2020), 26–82
Lang J., “Finsler Metrics on Surfaces Admitting Three Projective Vector Fields”, Differ. Geom. Appl., 69 (2020), 101590
Dunajski M., Mettler T., “Gauge Theory on Projective Surfaces and Anti-Self-Dual Einstein Metrics in Dimension Four”, J. Geom. Anal., 28:3 (2018), 2780–2811
Bagderina Yu.Yu., “Invariants of a family of scalar second-order ordinary differential equations for Lie symmetries and first integrals”, J. Phys. A-Math. Theor., 49:15 (2016), 155202
Kruglikov B., “Point Classification of Second Order ODEs: Tresse Classification Revisited and Beyond”, Differential Equations: Geometry, Symmetries and Integrability - the Abel Symposium 2008, Abel Symposia, 5, eds. Kruglikov B., Lychagin V., Straume E., Springer, 2009, 199–221
Bryant, RL, “A solution of a problem of Sophus Lie: normal forms of two-dimensional metrics admitting two projective vector fields”, Mathematische Annalen, 340:2 (2008), 437
R. A. Sharipov, “Newtonian normal shift in multidimensional Riemannian geometry”, Sb. Math., 192:6 (2001), 895–932

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	76
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