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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 182, Number 2, Pages 256–276
DOI: https://doi.org/10.4213/tmf8657 (Mi tmf8657) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Equivalence of second-order ordinary differential equations to Painlevé equations

Yu. Yu. Bagderina

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, Russia
Full-text PDF (537 kB) Citations (16)
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DOI: https://doi.org/10.4213/tmf8657
Abstract: All Painlevé equations except the first belong to one type of equations. In terms of invariants of these equations, we obtain criteria for the equivalence to the second Painlevé equation and to equation XXXIV in the list of $50$ equations without movable critical points. We find new necessary conditions of equivalence for the third and fourth and also special cases of the fifth and sixth Painlevé equations. We compare the invariants we use with invariants previously introduced by other authors and compare the obtained results.
Keywords: Painlevé equation, equivalence, invariant.
Funding agency Grant number
Russian Science Foundation 14-11-00078
Received: 17.02.2014
Revised: 11.08.2014
English version:
Theoretical and Mathematical Physics, 2015, Volume 182, Issue 2, Pages 211–230
DOI: https://doi.org/10.1007/s11232-015-0258-2
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. Yu. Bagderina, “Equivalence of second-order ordinary differential equations to Painlevé equations”, TMF, 182:2 (2015), 256–276; Theoret. and Math. Phys., 182:2 (2015), 211–230
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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