Paul Painlevé

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.

Painlevé Squares

Studies 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...

Painlevé ’ s theorem extended

we extend Painlevé’s determinateness theorem from the theory of ordinary differential equations in the complex domain allowing more general ’multiple-valued’ Cauchy’s problems. We study C0−continuability (near singularities) of solutions. Foreword and preliminaries In this paper we slightly improve Painlevé’s determinateness theorem (see [HIL], th.3.3.1), investigating the C0−continuability of ...

Four - Dimensional Painlevé

We find and study a five-parameter family of four-dimensional coupled Painlevé V systems with affine Weyl group symmetry of type D (1) 5 . We then give an explicit description of a confluence from those systems to a four-parameter family of four-dimensional coupled Painlevé III systems with affine Weyl group symmetry of type B (1) 4 . 0. Introduction It is well-known that the Painlevé systems P...