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TMF, 2014, Volume 179, Number 2, Pages 189–195 (Mi tmf8634)  

This article is cited in 5 scientific papers (total in 5 papers)

Euler integral symmetries for the confluent Heun equation and symmetries of the Painlevé equation PV

A. Ya. Kazakovab, S. Yu. Slavyanovc

a Saint Petersburg State University of Technology and Design, St. Petersburg, Russia
b St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, Russia
c St. Petersburg State University, St. Petersburg, Russia

Abstract: Euler integral symmetries relate solutions of ordinary linear differential equations and generate integral representations of the solutions in several cases or relations between solutions of constrained equations. These relations lead to the corresponding symmetries of the monodromy matrices for the differential equations. We discuss Euler symmetries in the case of the deformed confluent Heun equation, which is in turn related to the Painlevé equation PV. The existence of symmetries of the linear equations leads to the corresponding symmetries of the Painlevé equation of the Okamoto type. The choice of the system of linear equations that reduces to the deformed confluent Heun equation is the starting point for the constructions. The basic technical problem is to choose the bijective relation between the system parameters and the parameters of the deformed confluent Heun equation. The solution of this problem is quite large, and we use the algebraic computing system Maple for this.

Keywords: confluent Heun equation, Euler integral transform, monodromy, apparent singularity

DOI: https://doi.org/10.4213/tmf8634

Full text: PDF file (333 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 179:2, 543–549

Bibliographic databases:

Document Type: Article
Received: 23.12.2013

Citation: A. Ya. Kazakov, S. Yu. Slavyanov, “Euler integral symmetries for the confluent Heun equation and symmetries of the Painlevé equation PV”, TMF, 179:2 (2014), 189–195; Theoret. and Math. Phys., 179:2 (2014), 543–549

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Ya. Kazakov, “Integral symmetry for the confluent Heun equation with added apparent singularity”, J. Math. Sci. (N. Y.), 214:3 (2016), 268–276  mathnet  crossref  mathscinet
    2. J. Math. Sci. (N. Y.), 209:6 (2015), 910–921  mathnet  crossref
    3. A. M. Ishkhanyan, “Schrödinger potentials solvable in terms of the confluent Heun functions”, Theoret. and Math. Phys., 188:1 (2016), 980–993  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Kazakov A.Ya., “Confluent Heun Equation With Single Added Apparent Singularity”, Proceedings of the International Conference on Days on Diffraction 2016 (Dd), eds. Motygin O., Kiselev A., Kapitanova P., Goray L., Kazakov A., Kirpichnikova A., IEEE, 2016, 207–211  crossref  isi
    5. S. Yu. Slavyanov, A. A. Salatich, “Confluent Heun equation and confluent hypergeometric equation”, J. Math. Sci. (N. Y.), 232:2 (2018), 157–163  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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