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 (
Bei-Bei Hu, Ling Zhang, Tie-Cheng Xia
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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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Riemann-Hilbert boundary value problems in BMO classes for generalized analytic functions
Владикавказский математический журнал, 2011 В работе рассматривается разрешимость краевой задачи Римана - Гильберта в классе BMO для обобщенных аналитических функций в предположении, что коэффициент краевого условия принадлежит пространству мультипликаторов класса BMO. Ранее автором построены примеры, когда задача с неотрицательным индексом в такой наиболее стественной постановке неразрешима в ...
S. B. Klimentov
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The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann–Hilbert problems [PDF]
Inverse Problems, 2010 15 ...
Carlos Álvarez-Fernández +2 more
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Riemann-Hilbert Boundary Value Problem for Generalized Analytic Functions in Smirnov Classes
, 2014 The Riemann-Hilbert boundary value problem for generalized analytic functions in Smirnov classes is under consideration. The domain is supposed simply connected with Lyapunov or Radon boundary without cusps. In the work the special representation for generalized analytic functions of Smirnov classes is built.
SERGEY KLIMENTOV
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Generalization of I.Vekua's integral representations of holomorphic functions and their application to the Riemann–Hilbert–Poincaré problem [PDF]
Journal of Function Spaces and Applications, 2011 I. Vekua’s integral representations of holomorphic functions, whose m-th derivative (m≥0) is Hӧlder-continuous in a closed domain bounded by the Lyapunov curve, are generalized for analytic functions whose m-th derivative is representable by a Cauchy ...
Vakhtang Kokilashvili +1 more
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A Class of Nonlinear Generalized Riemann-Hilbert-Poincaré Problems for Holomorphic Functions
Zeitschrift für Analysis und ihre Anwendungen, 1987 By means of the theory of pseudo-monotone operators the existence of a solution of a class of nonlinear generalized Riemann-Hilbert-Poincaré problems for a holomorphic function in the unit disk is proved.
Lothar von Wolfersdorf
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مجلة الباحث الجامعي للعلوم الانسانيةتناولت هذه الدراسة اشتقاق معادلة التكامل من الدرجة الثانية لفريدهولم مع نواة نيومان التي جرى تعميمها و المتعلقة بمسألة ريمان-هيلبرت المتعلقة بمناطق الضرب المترابطة المفتوحة. أظهرت إشتقاق معادلة التكامل معادلات تكامل ذو حدود قابلة للحل بشكل فريد لمسألة دريتشلت المعدلة على مناطق الضرب المترابطة المفتوحة.
Mohamed M. S. Nasser
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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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