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

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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. Novikov^a, B. I. Suleimanov^b

^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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https://doi.org/10.4213/tmf8950

https://www.mathnet.ru/eng/tmf/v187/i1/p39

This publication is cited in the following 7 articles:

V. A. Pavlenko, “Solutions of Analogs of Time-Dependent Schrödinger Equations Corresponding to a Pair of $H^{2+2+1}$ Hamiltonian Systems in the Hierarchy of Degenerations of an Isomonodromic Garnier System”, Diff Equat, 60:1 (2024), 77
V. A Pavlenko, “REShENIYa ANALOGOV VREMENNYKh URAVNENIY ShR¨EDINGERA, SOOTVETSTVUYuShchIKh PARE GAMIL'TONOVYKh SISTEM ????2+2+1 IERARKhII VYROZhDENIY IZOMONODROMNOY SISTEMY GARN'E”, Differencialʹnye uravneniâ, 60:1 (2024), 76
V. A. Pavlenko, “Solutions of the analogues of time-dependent Schrödinger equations corresponding to a pair of $H^{3+2}$ Hamiltonian systems”, Theoret. and Math. Phys., 212:3 (2022), 1181–1192
B. I. Suleimanov, “Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom”, St. Petersburg Math. J., 33:6 (2022), 995–1009
V. A. Pavlenko, B. I. Suleimanov, “Solutions to analogues of non-stationary Schrödinger equations defined by isomonodromic Hamilton system $H^{2+1+1+1}$ ”, Ufa Math. J., 10:4 (2018), 92–102
V. A. Pavlenko, B. I. Suleimanov, ““Quantizations” of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$ ”, Ufa Math. J., 9:4 (2017), 97–107
B. I. Suleimanov, “Quantum aspects of the integrability of the third Painlevé equation and a non-stationary time Schrödinger equation with the Morse potential”, Ufa Math. J., 8:3 (2016), 136–154

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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