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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 485, Pages 187–194 (Mi znsl6877)  
Systems of first order ODE generating confluent Heun equations

A. A. Salatich, S. Yu. Slavyanov, O. L. Stesik

Saint Petersburg State University
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Abstract: Relation between linear second order equations being confluent Heun equations: biconfluent and triconfluent – and first order linear systems of equations which generate Painlevë equations is studied. The generation process is interpreted in physical terms as antiquantization.Technically the study includes manipulations with polynomials. The complexity of computations sometimes demands the use of Algebraic Computing Systems.
Key words and phrases: antiquantization, Heun class equation, confluent Heun class equations, Painlevé equations, isomonodromy property, apparent singularities.
Funding agency Grant number
Saint Petersburg State University ID-40847559
Received: 03.10.2019
Document Type: Article
UDC: 517.289, 517.923, 517.926
Language: Russian
Citation: A. A. Salatich, S. Yu. Slavyanov, O. L. Stesik, “Systems of first order ODE generating confluent Heun equations”, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Zap. Nauchn. Sem. POMI, 485, POMI, St. Petersburg, 2019, 187–194
Citation in format AMSBIB
\Bibitem{SalSlaSte19}
\by A.~A.~Salatich, S.~Yu.~Slavyanov, O.~L.~Stesik
\paper Systems of first order ODE generating confluent Heun equations
\inbook Representation theory, dynamical systems, combinatorial methods. Part~XXXI
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 485
\pages 187--194
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6877}
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