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TMF, 2015, Volume 182, Number 2, Pages 223–230 (Mi tmf8795)  

This article is cited in 6 scientific papers (total in 6 papers)

Polynomial degree reduction of a Fuchsian $2{\times}2$ system

S. Yu. Slavyanov

St. Petersburg State Universityy, St. Petersburg, Russia

Abstract: A Fuchsian $2{\times}2$ system generating the Painlevé equation $\mathrm P^6$ is acted on by a polynomial transformation similar to rotation in order to reduce the polynomial degree of matrices in the left- and the right-hand sides of the system. This clarifies the derivation of the Painlevé equation and the study of its symmetries.

Keywords: Fuchsian system, Painlevé equation

DOI: https://doi.org/10.4213/tmf8795

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English version:
Theoretical and Mathematical Physics, 2015, 182:2, 182–188

Bibliographic databases:

Received: 16.09.2014

Citation: S. Yu. Slavyanov, “Polynomial degree reduction of a Fuchsian $2{\times}2$ system”, TMF, 182:2 (2015), 223–230; Theoret. and Math. Phys., 182:2 (2015), 182–188

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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. S. Yu. Slavyanov, “Antiquantization and the corresponding symmetries”, Theoret. and Math. Phys., 185:1 (2015), 1522–1526  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. A. Mirjalili, M. Taki, “Noncommutative correction to the Cornell potential in heavy-quarkonium atoms”, Theoret. and Math. Phys., 186:2 (2016), 280–285  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. S. Yu. Slavyanov, D. F. Shat'ko, A. M. Ishkhanyan, T. A. Rotinyan, “Generation and removal of apparent singularities in linear ordinary differential equations with polynomial coefficients”, Theoret. and Math. Phys., 189:3 (2016), 1726–1733  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. S. Yu. Slavyanov, “Symmetries and apparent singularities for the simplest Fuchsian equations”, Theoret. and Math. Phys., 193:3 (2017), 1754–1760  mathnet  crossref  crossref  adsnasa  isi  elib
    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
    6. P. V. Bibikov, “On Differential Invariants and Classification of Ordinary Differential Equations of the Form $y-A(x,y)y'+B(x,y)$”, Math. Notes, 104:2 (2018), 167–175  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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