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TMF, 2016, Volume 187, Number 1, Pages 39–57 (Mi tmf8950)  

This article is cited in 3 scientific papers (total in 3 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

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).


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

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English version:
Theoretical and Mathematical Physics, 2016, 187:1, 479–496

Bibliographic databases:

Received: 22.04.2015
Revised: 24.06.2015

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet  isi  elib
    2. V. A. Pavlenko, B. I. Suleimanov, ““Quantizations” of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$”, Ufa Math. J., 9:4 (2017), 97–107  mathnet  crossref  isi  elib
    3. 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  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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