Painlevé Squares
نویسنده
چکیده
منابع مشابه
Painlevé test and the first Painlevé hierarchy
Starting from the first Painlevé equation, Painlevé type equations of higher order are obtained by using the singular point analysis.
متن کاملJustification of the existence of a group of asymptotics of the general fifth Painlevé transcendent
There are several existing ways in developing the asymptotics of the Painlevé transcendents. But it is always a hard task to justify the existence of these asymptotics. In this note, we apply the successive approximation to the general fifth Painlevé equation and rigorously prove the existence of a group of asymptotics of its solutions. 1. Introduction. The mathematical and physical significanc...
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 کامل1 8 Se p 20 00 DEFORMATION OF OKAMOTO – PAINLEVÉ PAIRS AND PAINLEVÉ EQUATIONS
In this paper, we introduce the notion of generalized rational Okamoto–Painlevé pair (S, Y ) by generalizing the notion of the spaces of initial conditions of Painlevé equations. After classifying those pairs, we will establish an algebro-geometric approach to derive the Painlevé differential equations from the deformation of Okamoto–Painlevé pairs by using the local cohomology groups. Moreover...
متن کاملON THE IDENTITY OF TWO q-DISCRETE PAINLEVÉ EQUATIONS AND THEIR GEOMETRICAL DERIVATION
One of the characteristics of discrete Painlevé equations is that they may possess more than one canonical form. Indeed we often encounter equations which are written as a system involving several dependent variables. Since by definition the discrete Painlevé equations are second-order mappings, these multicomponent systems include equations which are local. It is then straightforward, if some ...
متن کامل