Equivalence of second-order ordinary differential equations to Painlevé equations

Bagderina, Yu. Yu.

doi:10.1007/s11232-015-0258-2

Cited by 16 publications

(11 citation statements)

References 17 publications

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“…Yu. Bagderina in [20], where she compares her results with the previously known results from [3][4][5]. The formula (8.1) is evidently in agreement with the second formula (7.2) from [20].…”

Section: Scalar Invariantssupporting

confidence: 66%

Umbilical and zero curvature equations in a class of second order ODE's

Шарипов¹

2017

Preprint

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The class of second order ODE's cubic with respect to the first order derivative is considered. Using geometric structures associated with these equations, the subclasses of umbilical equations, zero mean curvature equations, and zero Gaussian curvature equations are defined. Zero mean curvature equations are studied within the framework of the first case of intermediate degeneration with the stress on their pseudoscalar and scalar invariants.

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Section: Scalar Invariantssupporting

confidence: 66%

Umbilical and zero curvature equations in a class of second order ODE's

Шарипов¹

2017

Preprint

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“…However, in [5] there are no explicit formulas expressing I 1 , I 2 , I 3 through I Bgd 1 and I Bgd 2 . Some formulas of this sort are given in [13], but again for the case Ω = 0, which is outside our present intersection class ShrID1 ∩ BgdET2.…”

Section: Discussionmentioning

confidence: 99%

Comparison of two classifications of a class of ODE's in the first case of intermediate degeneration

Sharipov

2017

Preprint

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“…For various results on classifying classes of second-order ordinary differential equations, including Painlevé equations, see Babich and Bordag [12], Bagderina [13,15,16,17,18], Bagderina and Tarkhanov [19], Berth and Czichowski [22], Hietarinta and Dryuma [78], Kamran, Lamb and Shadwick [88], Kartak [90,91,92,93], Kossovskiy and Zaitsev [97], Milson and Valiquette [106], Valiquette [139] and Yumaguzhin [145]. Most of these studies are concerned with the invariance of second-order ordinary differential equations of the form…”

Section: Painlevé Equivalence Problemmentioning

confidence: 99%