Quantum Painlevé equations: from continuous to discrete.
Quiver varieties with multiplicities, Weyl groups of non-symmetric Kac-Moody algebras, and Painlevé equations.
Rational solutions of the Sasano system of type .
Regular coordinates and reduction of deformation equations for Fuchsian systems
For a Fuchsian system , (F) being distinct points in ℂ and , the number α of accessory parameters is determined by the spectral types , where . We call the set of α parameters a regular coordinate if all entries of the are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues of the matrices...
Supersymmetric quantum mechanics and Painlevé IV equation.
Sur certaines solutions particulières transcendantes des équations d'Einstein
Symmetries in connection preserving deformations.
The Lamé family of connections on the projective line
This paper deals with rank two connections on the projective line having four simple poles with prescribed local exponents 1/4 and . This Lamé family of connections has been extensively studied in the literature. The differential Galois group of a Lamé connection is never maximal : it is either dihedral (finite or infinite) or reducible. We provide an explicit moduli space of those connections having a free underlying vector bundle and compute the algebraic locus of those reducible connections....
The lattice structure of connection preserving deformations for -Painlevé equations I.
The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI
Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...
Universal isomonodromic deformations of meromorphic rank 2 connections on curves
We consider tracefree meromorphic rank 2 connections over compact Riemann surfaces of arbitrary genus. By deforming the curve, the position of the poles and the connection, we construct the global universal isomonodromic deformation of such a connection. Our construction, which is specific to the tracefree rank 2 case, does not need any Stokes analysis for irregular singularities. It is thereby more elementary than the construction in arbitrary rank due to B. Malgrange and I. Krichever and it includes...
Zur Wertverteilung der Lösungen der vierten Painlevéschen Differentialgleichung.
Асимптотическое описание решений четвертого уравнения Пенлеве на аналогах лучей Стокса
Второе уравнение Пенлеве в одной задаче о нелинейных эффектах вблизи каустик
Вычисление непертурбативного параметра в матричной модели
Континуальный предел в эрмитовой матричной модели
О симмeтричных решениях для первого и второго уравнений Пенлеве
Предельный переход
Скейлинговые пределы для второго трансцендента Пенлеве
Слабонелинейные решения уравнения