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Some addition to the generalized Riemann-Hilbert problem [PDF]
Annales de la Faculté des sciences de Toulouse : Mathématiques, 2008 We give some additions to the article "On the generalized Riemann-Hilbert problem with irregular singularities" by Bolibruch, Malek, Mitschi (math/0410483).
Gontsov, R. R., Vyugin, I. V.
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Analytical Method for Generalized Nonlinear Schrödinger Equation with Time-Varying Coefficients: Lax Representation, Riemann-Hilbert Problem Solutions [PDF]
Mathematics, 2022 In this paper, a generalized nonlinear Schrödinger (gNLS) equation with time-varying coefficients is analytically studied using its Lax representation and the associated Riemann-Hilbert (RH) problem equipped with a symmetric scattering matrix in the ...
Bo Xu, Sheng Zhang
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Nonlinear Riemann-Hilbert Problems for Generalized Analytic Functions [PDF]
Functiones et Approximatio Commentarii Mathematici, 2009 In this study we deal with the nonlinear Riemann--Hilbert problem (in short (RHP)) for generalized analytic functions in multiply connected domains. Using a similarity principle for multiply connected domains (presented here for the first time), we reduce the nonlinear RHP for generalized analytic functions to a corresponding nonlinear RHP for ...
Messoud Efendiev, Wolfgang L. Wendland
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Generalized orthogonal polynomials, discrete KP and Riemann-Hilbert problems [PDF]
Communications in Mathematical Physics, 1999 Classically, a single weight on an interval of the real line leads to moments, orthogonal polynomials and tridiagonal matrices. Appropriately deforming this weight with times t=(t_1,t_2,...), leads to the standard Toda lattice and tau-functions ...
Adler, Mark, van Moerbeke, Pierre
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On the generalized Riemann–Hilbert problem with irregular singularities
Expositiones Mathematicae, 2005 We give sufficient conditions, on data including the monodromy representation, the Stokes matrices and the Poincare ranks at prescribed singularities, to solve the generalized Riemann-Hilbert problem with irregular singularities. We recover in particular the irreducibility condition on the monodromy given by Bolibrukh and Kostov in the classical case ...
A.A. Bolibruch +2 more
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On the Riemann–Hilbert problem of a generalized derivative nonlinear Schrödinger equation [PDF]
Communications in Theoretical Physics, 2020 Abstract In this work, we present a unified transformation method directly by using the inverse scattering method for a generalized derivative nonlinear Schrödinger (DNLS) equation. By establishing a matrix Riemann–Hilbert problem and reconstructing potential function q(x, t) from eigenfunctions
Beibei Hu, Ling Zhang, Tiecheng Xia
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Two-component generalized Ragnisco-Tu equation and the Riemann-Hilbert problem [PDF]
Theoretical and Mathematical Physics, 2020 Using the Riemann–Hilbert approach, we investigate the two-component generalized Ragnisco–Tu equation. The modified equation is integrable in the sense that a Lax pair exists, but its explicit solutions have some distinctive properties. We show that the explicit one-wave solution is unstable and the two-wave solution preserves only the phase shift but ...
Lin Lin Wang, Caiqin Song, Junyi Zhu
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The solvability of a kind of generalized Riemann–Hilbert problems on function spaces $H_{\ast }$ [PDF]
Journal of Inequalities and Applications, 2020 Abstract In this paper, we study a kind of generalized Riemann–Hilbert problems (R-HPs) with several unknown functions in strip domains. We mainly discuss methods of solving R-HPs with two unknown functions and obtain general solutions and conditions of solvability on function spaces $H_{\ast }$ H ∗ .
Pingrun Li
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The Riemann Hilbert problem for generalized Q-holomorphic functions
Turkish Journal of Mathematics, 2010 In this work, the classical Riemann Hilbert boundary value problem is extended to generalized Q-holomorphic functions.
Sezayi Hızlıyel, MEHMET ÇAĞLIYAN
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The Riemann–Hilbert problem and the generalized Neumann kernel on multiply connected regions
Journal of Computational and Applied Mathematics, 2007 AbstractThis paper presents and studies Fredholm integral equations associated with the linear Riemann–Hilbert problems on multiply connected regions with smooth boundary curves. The kernel of these integral equations is the generalized Neumann kernel. The approach is similar to that for simply connected regions (see [R. Wegmann, A.H.M.
R. Wegmann, Mohamed M. S. Nasser
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