This article is cited in 17 papers

Isomonodromic deformations of Heun and Painlevé equations

S. Yu. Slavyanov

Saint-Petersburg State University

Abstract: Continuing the study of the relationship between the Heun and the Painlevé classes of equations reported in two previous papers, we formulate and prove the main theorem expressing this relationship. We give a Hamiltonian interpretation of the isomonodromic deformation condition and propose an alternative classification of the Painlevé equations, which includes ten equations.

Received: 07.10.1999

DOI: 10.4213/tmf611

 English version: Theoretical and Mathematical Physics, 2000, 123:3, 744–753

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