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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 173, Number 2, Pages 245–267
DOI: https://doi.org/10.4213/tmf8320 (Mi tmf8320) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Solution of the equivalence problem for the Painlevé IV equation

V. V. Kartakab

a Ufa State Aviation Technical University, Ufa, Russia
b Bashkir State University, Ufa, Russia
Full-text PDF (484 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf8320
Abstract: We solve the equivalence problem for the Painlevé IV equation, formulating the necessary and sufficient conditions in terms of the invariants of point transformations for an arbitrary second-order differential equation to be equivalent to the Painlevé IV equation. We separately consider three pairwise nonequivalent cases: both equation parameters are zero, $a=b=0$; only one parameter is zero, $b=0$; and the parameter $b\ne0$. In all cases, we give an explicit point substitution transforming an equation satisfying the described test into the Painlevé IV equation and also give expressions for the equation parameters in terms of invariants.
Keywords: Painlevé equation, point transformation, equivalence problem, invariant.
Received: 29.12.2011
Revised: 13.06.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 173, Issue 2, Pages 1541–1564
DOI: https://doi.org/10.1007/s11232-012-0132-4
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Kartak, “Solution of the equivalence problem for the Painlevé IV equation”, TMF, 173:2 (2012), 245–267; Theoret. and Math. Phys., 173:2 (2012), 1541–1564
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v173/i2/p245
    • This publication is cited in the following 8 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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