This article is firstly a historic review of the theory of Riemann–Hilbert problems with
particular emphasis placed on their original appearance in the context of Hilbert's 21st …

We compute asymptotics for Hankel determinants and orthogonal polynomials with respect
to a discontinuous Gaussian weight, in a critical regime where the discontinuity is close to …

In this paper some open problems for Painlevé equations are discussed. In particular the
following open problems are described:(i) the Painlevé equivalence problem;(ii) notation for …

We consider real-valued solutions u= u (x| s), x∈ R, of the second Painlevé equation uxx=
xu+ 2 u 3 which are parameterized in terms of the monodromy data s≡(s 1, s 2, s 3)⊂ C 3 of …

We formulate the generic τ-function of the homogeneous Painlevé II equation as a Fredholm
determinant of an integrable (Its–Izergin–Korepin–Slavnov) operator. The τ-function …

We consider the second Painlev\'e equation $$ u"(x)= 2u^ 3 (x)+ xu (x)-\alpha, $$ where
$\alpha $ is a nonzero constant. Using the Deift-Zhou nonlinear steepest descent method for …

This paper is the first in a forthcoming series of works where the authors study the global
asymptotic behavior of the radial solutions of the 2D periodic Toda equation of type A n. The …

Asymptotics of the deformed higher order Airy-kernel determinants and applications Page 1
Nonlinearity PAPER Asymptotics of the deformed higher order Airykernel determinants and …

Abstract We consider the Clarkson–McLeod solutions of the fourth Painlevé equation. This
family of solutions behave like κ D α− 1 2 2 (2 x) as x→+∞, where κ is an arbitrary real …

Motivated by the simplest case of tt*-Toda equations, we study the large and small x
asymptotics for x> 0 of real solutions of the sinh-Godron Painlevé III (D 6) equation. These …