Geodesic
``Quantizations'' of the~second Painlev\'e equation and the~problem of
Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 364-377

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We show that the known Flaschka–Newell $L$–$A$ pair for the second Painlevé equation gives solutions to linear evolutionary equations similar to the quantum Schrödinger equations. Using the Fourier transform for distributions, we derive this pair from the classical Garnier pair.
Keywords: quantum Schrödinger equation, Hamiltonian, Painlevé equations
Mots-clés : isomonodromic deformation. 
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     author = {B. I. Suleimanov},
     title = {``Quantizations'' of the~second {Painlev\'e} equation and the~problem of},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a3/}
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B. I. Suleimanov. ``Quantizations'' of the~second Painlev\'e equation and the~problem of. Teoretičeskaâ i matematičeskaâ fizika, Tome 156 (2008) no. 3, pp. 364-377. http://geodesic.mathdoc.fr/item/TMF_2008_156_3_a3/