Generalization of Okamoto's Equation to Arbitrary 2×2 Schlesinger System
Joint Authors
Samtleben, Henning
Korotkin, Dmitry
Source
Advances in Mathematical Physics
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-10-15
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
The 2×2 Schlesinger system for the case of four regular singularities is equivalent to the Painlevé VI equation.
The Painlevé VI equation can in turn be rewritten in the symmetric form of Okamoto's equation; the dependent variable in Okamoto's form of the PVI equation is the (slightly transformed) logarithmic derivative of the Jimbo-Miwa tau-function of the Schlesinger system.
The goal of this note is twofold.
First, we find a universal formulation of an arbitrary Schlesinger system with regular singularities in terms of appropriately defined Virasoro generators.
Second, we find analogues of Okamoto's equation for the case of the 2×2 Schlesinger system with an arbitrary number of poles.
A new set of scalar equations for the logarithmic derivatives of the Jimbo-Miwa tau-function is derived in terms of generators of the Virasoro algebra; these generators are expressed in terms of derivatives with respect to singularities of the Schlesinger system.
American Psychological Association (APA)
Korotkin, Dmitry& Samtleben, Henning. 2009. Generalization of Okamoto's Equation to Arbitrary 2×2 Schlesinger System. Advances in Mathematical Physics،Vol. 2009, no. 2009, pp.1-14.
https://search.emarefa.net/detail/BIM-473439
Modern Language Association (MLA)
Korotkin, Dmitry& Samtleben, Henning. Generalization of Okamoto's Equation to Arbitrary 2×2 Schlesinger System. Advances in Mathematical Physics No. 2009 (2009), pp.1-14.
https://search.emarefa.net/detail/BIM-473439
American Medical Association (AMA)
Korotkin, Dmitry& Samtleben, Henning. Generalization of Okamoto's Equation to Arbitrary 2×2 Schlesinger System. Advances in Mathematical Physics. 2009. Vol. 2009, no. 2009, pp.1-14.
https://search.emarefa.net/detail/BIM-473439
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473439