Results 81 to 90 of about 552 (182)

Solvability of some classes of singular integral equations of convolution type via Riemann–Hilbert problem

Journal of Inequalities and Applications, 2019
In this paper, we study methods of solution for some kinds of convolution type singular integral equations with Cauchy kernel. By means of the classical boundary value problems for analytic functions and of the theory of complex analysis, we deal with ...
Pingrun Li
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Optical solitons and their propagations in a time-varying coefficient modified nonlinear Schrödinger equation with non-zero boundary conditions via Riemann–Hilbert method

Results in Physics
In this article, a time-varying coefficient modified nonlinear Schrödinger equation (tvcmNLSE) with non-zero boundary conditions (NZBCs) at infinity, phase term of which contains time-varying coefficients, is proposed to describe the nonlinear ...
Xiuyan Wei, Yinan Chen, Sheng Zhang
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The Riemann–Hilbert Problem for Holonomic Systems

Publications of the Research Institute for Mathematical Sciences, 1984
Let X be a paracompact complex manifold of dimension n, \(X_{{\mathbb{R}}}\) the underlying real analytic manifold and \(\bar X\) the complex conjugate of X. Let \({\mathcal D}_ X\) and \({\mathcal O}_ X\) be the sheaf of differential operators and holomorphic functions. The ring \({\mathcal A}_{X_{{\mathbb{R}}}}\) and \({\mathcal D}_{X_{{\mathbb{R}}}}\
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An approach for constructing coefficients of degenerate elliptic complex equations

Electronic Journal of Differential Equations, 2013
This article deals with the inverse problem for degenerate elliptic systems of first order equations with Riemann-Hilbert type map in simply connected domains.
Guo Chun Wen
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Dynamical Behavior Analysis of Generalized Chen–Lee–Liu Equation via the Riemann–Hilbert Approach

Fractal and Fractional
In this paper, we investigate the dynamics of the generalized Chen–Lee–Liu (gCLL) equation utilizing the Riemann–Hilbert method to derive its N-soliton solution.
Wenxia Chen, Chaosheng Zhang, Lixin Tian
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Initial Boundary Value Problem for the Coupled Kundu Equations on the Half-Line

Axioms
In this article, the coupled Kundu equations are analyzed using the Fokas unified method on the half-line. We resolve a Riemann–Hilbert (RH) problem in order to illustrate the representation of the potential function in the coupled Kundu equations.
Jiawei Hu, Ning Zhang
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Nonlinear Riemann-Hilbert Problems

, 2009
Riemann-Hilbert-Probleme sind Randwertaufgaben für im Einheitskreis $\mathbb D$ holomorphe Funktionen $w$, deren Randwerte $w(t)$ auf gewissen Kurven $M_t$ liegen sollen. Ein Teil der Untersuchungen ist dem Fall explizit gegebener Kurven gewidmet. Dabei werden bekannte Resultate über glatte Kurven auf stetige Restriktionskurven erweitert, und die ...
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Solution of the modified Helmholtz equation using mixed boundary conditions in an equilateral triangle

Partial Differential Equations in Applied Mathematics
The modified Helmholtz equation qxx+qyy−4β2q=0, is one of the basic equations of classical mathematical physics. In this paper we have obtained the solution of the boundary-value problems for the modified Helmholtz equation in an equilateral triangle. An
Pratul Gadagkar, Subhash Kendre, Pooja Paratane   +2 more
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From Quantum Curves to Topological String Partition Functions. [PDF]

Commun Math Phys, 2023
Coman I, Pomoni E, Teschner J.
europepmc   +1 more source

ON THE DISCONTINUOUS RIEMANN-HILBERT PROBLEM

Demonstratio Mathematica, 1970
Łubowicz, Henryk, Wieprzkowicz, Bohdan
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