A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators
We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.
Analytical solution of a general boundary value problem for a BKW-equation.
Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.
Déformations isomonodromiques des singularités régulières
Geometry and analytic theory of Frobenius manifolds.
Initial boundary value problem for the mKdV equation on a finite interval
We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex -plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at and . We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms of spectral...
Le problème de Riemann Hilbert sur une variété analytique complexe
Le problème de Riemann Hilbert sur une variété analytique complexe
Le problème de Riemann-Hilbert sur une variété complexe s’énonce de la manière suivante : soit un sous-ensemble analytique de de codimension un en chacun de ses points et une représentation de dans . Existe-t-il un système de Pfaff du type de Fuchs où (J. de Math. Pures et Appl., 47, (1968)) dont la monodromie soit la classe de la représentation ?On montre en particulier que si est une variété de Stein contractile et si les composantes irréductibles de sont sans singularités...
Long time asymptotics of the Camassa–Holm equation on the half-line
We study the long-time behavior of solutions of the initial-boundary value (IBV) problem for the Camassa–Holm (CH) equation on the half-line . The paper continues our study of IBV problems for the CH equation, the key tool of which is the formulation and analysis of associated Riemann–Hilbert factorization problems. We specify the regions in the quarter space-time plane , having qualitatively different asymptotic pictures, and give the main terms of the asymptotics in terms of spectral data...
Loop spaces and Riemann-Hilbert problems
We present a survey of recent results concerned with generalizations of the classical Riemann-Hilbert transmission problem in the context of loop spaces. Specifically, we present a general formulation of a Riemann-Hilbert problem with values in an almost complex manifold and illustrate it by discussing two particular cases in more detail. First, using the generalized Birkhoff factorization theorem of A. Pressley and G. Segal we give a criterion of solvability for generalized Riemann-Hilbert problems...
Nonlinear Riemann Boundary Value Problems for a Nonlinear Elliptic System in the Plane.
On a generalization of Hilbert's 21st problem
On a mixed boundary values problem for Lavrentev type equations
On factorization and partial indices of unitary matrix-functions of one class.
On the associative Nijenhuis relation.
On the Riemann-Hilbert problem in the domain with a nonsmooth boundary.
Problème de Riemann généralisé pour une sorte de systémes des cables
Resolution of the Cauchy problem for several hyperbolic systems arising in chemical engineering
Riemann-Hilbert problem and solvability of differential equations.