Geodesic
Point equivalence of second-order ordinary differential equations to the~fifth Painlev\'e equation with one and two nonzero parameters
Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 339-352

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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
Mots-clés : equivalence, invariant. 
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     author = {Yu. Yu. Bagderina},
     title = {Point equivalence of second-order ordinary differential equations to the~fifth {Painlev\'e} equation with one and two nonzero parameters},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {339--352},
     publisher = {mathdoc},
     volume = {202},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a1/}
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Yu. Yu. Bagderina. Point equivalence of second-order ordinary differential equations to the~fifth Painlev\'e equation with one and two nonzero parameters. Teoretičeskaâ i matematičeskaâ fizika, Tome 202 (2020) no. 3, pp. 339-352. http://geodesic.mathdoc.fr/item/TMF_2020_202_3_a1/