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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 1, Pages 39–57
DOI: https://doi.org/10.4213/tmf8950 (Mi tmf8950) 		 
This article is cited in 7 scientific papers (total in 7 papers)

"Quantization" of an isomonodromic Hamiltonian Garnier system with two degrees of freedom

D. P. Novikova, B. I. Suleimanovb

a Omsk State Technical University, Omsk, Russia
b Institute of Mathematics with Computing Centre, RAS, Ufa, Russia
Full-text PDF (513 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf8950
Abstract: We construct solutions of analogues of a time-dependent Schrödinger equation corresponding to an isomonodromic polynomial Hamiltonian of a Garnier system with two degrees of freedom. The solutions are determined by solutions of linear differential equations whose compatibility condition is the given Garnier system. With explicit substitutions, these solutions reduce to solutions of the Belavin–Polyakov–Zamolodchikov equations with four times and two spatial variables.
Keywords: Schrödinger equation, Hamiltonian, isomonodromic deformation, Garnier system, Belavin–Polyakov–Zamolodchikov equation, Painlevé equation.
Funding agency Grant number
Russian Science Foundation 14-11-00078
The research of B. I. Suleimanov is funded by a grant from the Russian Scientific Foundation (Project No. 14-11-00078).
Received: 22.04.2015
Revised: 24.06.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 1, Pages 479–496
DOI: https://doi.org/10.1134/S0040577916040048
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: D. P. Novikov, B. I. Suleimanov, “"Quantization" of an isomonodromic Hamiltonian Garnier system with two degrees of freedom”, TMF, 187:1 (2016), 39–57; Theoret. and Math. Phys., 187:1 (2016), 479–496
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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