منابع مشابه
Galois Theory and Painlevé Equations
— The paper consists of two parts. In the first part, we explain an excellent idea, due to mathematicians of the 19-th century, of naturally developing classical Galois theory of algebraic equations to an infinite dimensional Galois theory of nonlinear differential equations. We show with an instructive example how we can realize the idea of the 19-th century in a rigorous framework. In the sec...
متن کاملStudies on the Painlevé equations V , third Painlevé
By means of geometrical classification ([22]) of space of initial conditions, it is natural to consider the three types, PIII(D6), PIII(D7) and PIII(D8), for the third Painlevé equation. The fourth article of the series of papers [17] on the Painlevé equations is concerned with PIII(D6), generic type of the equation. The other two types, PIII(D7) and PIII(D8) are obtained as degeneration from P...
متن کاملDiscrete Painlevé Equations and Random Matrix Averages
The τ-function theory of Painlevé systems is used to derive recurrences in the rank n of certain random matrix averages over U (n). These recurrences involve auxilary quantities which satisfy discrete Painlevé equations. The random matrix averages include cases which can be interpreted as eigenvalue distributions at the hard edge and in the bulk of matrix ensembles with unitary symmetry. The re...
متن کاملPainlevé equations and deformations of rational surfaces with rational double points ∗ †
In this paper we give an answer to the fundamental questions about the Painlevé equations. Where do the Bäcklund transformations come from? Our approach depends on the geometry of the projective surface constructed by Okamoto and reviewed in [U2]. The Painlevé equations were discovered around 1900 in the pursuit of special functions. Painlevé and Gambier classified algebraic differential equati...
متن کاملSchlesinger Transformations for Bonnet Surfaces
Bonnet surfaces, i.e. surfaces in Euclidean 3-space, which admits a one-parameter family of isometries preserving the mean curvature function, can be described in terms of solutions of some special Painlev e equations. The goal of this work is to use the well-known Schlesinger transformations for solutions of Painlev e VI equations to create new Bonnet surfaces from a known one.
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ژورنال
عنوان ژورنال: Journal für die reine und angewandte Mathematik (Crelles Journal)
سال: 1998
ISSN: 0075-4102,1435-5345
DOI: 10.1515/crll.1998.061