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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
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.
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
Linking options:
https://www.mathnet.ru/eng/tmf8950https://doi.org/10.4213/tmf8950 https://www.mathnet.ru/eng/tmf/v187/i1/p39
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Abstract page: | 482 | Full-text PDF : | 196 | References: | 91 | First page: | 31 |
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