This article is cited 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.

Received: 16.09.2014

DOI: 10.4213/tmf8795

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

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