New contiguity relation of the sixth Painlevé equation from a truncation
نویسندگان
چکیده
منابع مشابه
Dynamics of the Sixth Painlevé Equation
— The sixth Painlevé equation is hiding extremely rich geometric structures behind its outward appearance. In this article, we give a complete picture of its dynamical nature based on the Riemann-Hilbert approach recently developed by the authors and using various techniques from algebraic geometry. A large part of the contents can be extended to Garnier systems, while this article is restricte...
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The sixth Painlevé equation arises from a Drinfel’d-Sokolov hierarchy of type D (1) 4 by similarity reduction. 2000 Mathematics Subject Classification: 34M55, 17B80, 37K10. Introduction The Drinfel’d-Sokolov hierarchies are extensions of the KdV (or mKdV) hierarchy [DS]. It is known that their similarity reductions imply several Painlevé equations [AS, KK1, NY1]. For the sixth Painlevé equation...
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0. Introduction 0.1. Three approaches to the Painlevé equations. The differential equations studied in this paper form a family PVI α,β,γ,δ depending on four parameters α, β, γ, δ, and classically written as: d 2 X dt 2 = 1 2 1 X + 1 X − 1 + 1 X − t dX dt 2 − 1 t + 1 t − 1 + 1 X − t dX dt + + X(X − 1)(X − t) t 2 (t − 1) 2 α + β t X 2 + γ t − 1 (X − 1) 2 + δ t(t − 1) (X − t) 2. (0.1) They were d...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2002
ISSN: 0167-2789
DOI: 10.1016/s0167-2789(01)00372-4