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

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Teoreticheskaya i Matematicheskaya Fizika, 2015, Volume 182, Number 2, Pages 223–230
DOI: https://doi.org/10.4213/tmf8795 (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

Full-text PDF (328 kB) Citations (6)

References:

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

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.

Received: 16.09.2014

English version:
Theoretical and Mathematical Physics, 2015, Volume 182, Issue 2, Pages 182–188
DOI: https://doi.org/10.1007/s11232-015-0256-4

Bibliographic databases:

Document Type: Article

Language: Russian

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

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf8795

https://doi.org/10.4213/tmf8795

https://www.mathnet.ru/eng/tmf/v182/i2/p223

This publication is cited in the following 6 articles:

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
S. Yu. Slavyanov, “Symmetries and apparent singularities for the simplest Fuchsian equations”, Theoret. and Math. Phys., 193:3 (2017), 1754–1760
S. Yu. Slavyanov, A. A. Salatich, “Confluent Heun equation and confluent hypergeometric equation”, J. Math. Sci. (N. Y.), 232:2 (2018), 157–163
A. Mirjalili, M. Taki, “Noncommutative correction to the Cornell potential in heavy-quarkonium atoms”, Theoret. and Math. Phys., 186:2 (2016), 280–285
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
S. Yu. Slavyanov, “Antiquantization and the corresponding symmetries”, Theoret. and Math. Phys., 185:1 (2015), 1522–1526

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	364
Full-text PDF :	165
References:	62
First page:	22

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