Geodesic
A Lagrangian description of the higher-order Painlevé equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5

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We derive the Lagrangians of the higher-order Painlevé equations using Jacobi’s last multiplier technique. Some of these higher-order differential equations display certain remarkable properties like passing the Painlevé test and satisfy the conditions stated by Jurás̆, thus allowing for a Lagrangian description. 
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     title = {A {Lagrangian} description of the higher-order {Painlev\'e} equations},
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A. Choudhury; P. Guha; N. A. Kudryashov. A Lagrangian description of the higher-order Painlevé equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_5_a10/