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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 156, Number 3, Pages 364–377
DOI: https://doi.org/10.4213/tmf6253 (Mi tmf6253) 		 
This article is cited in 22 scientific papers (total in 22 papers)

“Quantizations” of the second Painlevé equation and the problem of the equivalence of its $L$–$A$ pairs

B. I. Suleimanov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
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DOI: https://doi.org/10.4213/tmf6253
Abstract: 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, isomonodromic deformation.
Received: 23.05.2007
Revised: 09.01.2008
English version:
Theoretical and Mathematical Physics, 2008, Volume 156, Issue 3, Pages 1280–1291
DOI: https://doi.org/10.1007/s11232-008-0106-8
Bibliographic databases:
Language: Russian
Citation: B. I. Suleimanov, ““Quantizations” of the second Painlevé equation and the problem of the equivalence of its $L$–$A$ pairs”, TMF, 156:3 (2008), 364–377; Theoret. and Math. Phys., 156:3 (2008), 1280–1291
Citation in format AMSBIB
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    • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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