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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 202, Number 3, Pages 339–352
DOI: https://doi.org/10.4213/tmf9802 (Mi tmf9802) 		 
Point equivalence of second-order ordinary differential equations to the fifth Painlevé equation with one and two nonzero parameters

Yu. Yu. Bagderina

Institute of Mathematics with Computing Centre, Ufa Federal Research Centre of Russian Academy of Science, Ufa, Russia
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DOI: https://doi.org/10.4213/tmf9802
Abstract: We consider the problem of the equivalence of scalar second-order ordinary differential equations under invertible point transformations. To solve this problem in the case of Painlevé equations, we use previously constructed invariants of a family of equations whose right-hand sides have a cubic nonlinearity in the first derivative. We obtain the conditions for point equivalence to the fifth Painlevé equation if two or three of its parameters are equal to zero.
Keywords: Painlevé equation, equivalence, invariant.
Received: 30.08.2019
Revised: 27.09.2019
English version:
Theoretical and Mathematical Physics, 2020, Volume 202, Issue 3, Pages 295–308
DOI: https://doi.org/10.1134/S0040577920030022
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Document Type: Article
Language: Russian
Citation: Yu. Yu. Bagderina, “Point equivalence of second-order ordinary differential equations to the fifth Painlevé equation with one and two nonzero parameters”, TMF, 202:3 (2020), 339–352; Theoret. and Math. Phys., 202:3 (2020), 295–308
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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