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“Quantization” of an isomonodromic Hamiltonian Garnier system with two degrees of freedom

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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.

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Authors and Affiliations

  1. Omsk State Technical University, Omsk, Russia

    D. P. Novikov

  2. Institute of Mathematics, RAS, Ufa, Russia

    B. I. Suleimanov

Authors
  1. D. P. Novikov
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  2. B. I. Suleimanov
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Correspondence to B. I. Suleimanov.

Additional information

The research of B. I. Suleimanov is funded by a grant from the Russian Scientific Foundation (Project No. 14-11-00078).

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 187, No. 1, pp. 39–57, April, 2016.

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Novikov, D.P., Suleimanov, B.I. “Quantization” of an isomonodromic Hamiltonian Garnier system with two degrees of freedom. Theor Math Phys 187, 479–496 (2016). https://doi.org/10.1134/S0040577916040048

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  • DOI: https://doi.org/10.1134/S0040577916040048

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