Results 11 to 20 of about 45,379 (233)
A Riemann–Hilbert problem for biorthogonal polynomials
Journal of Computational and Applied Mathematics, 2005 We characterize the biorthogonal polynomials that appear in the theory of coupled random matrices via a Riemann-Hilbert problem. Our Riemann-Hilbert problem is different from the ones that were proposed recently by Ercolani and McLaughlin, Kapaev, and Bertola et al. We believe that our formulation may be tractable to asymptotic analysis.
Kuijlaars, A.B.J., McLaughlin, K.T.-R.
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Riemann-Hilbert problems [PDF]
, 2019 These lectures introduce the method of nonlinear steepest descent for Riemann-Hilbert problems. This method finds use in studying asymptotics associated to a variety of special functions such as the Painlev equations and orthogonal polynomials, in solving the inverse scattering problem for certain integrable systems, and in proving universality for ...
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Hilbert boundary value problem for generalized analytic functions with a singular line [PDF]
E3S Web of Conferences, 2021 In this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index and a boundary condition on a circle for a generalized Cauchy-Riemann equation with a singular coefficient.
Shabalin Pavel, Faizov Rafael
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Mathematics, 2022 In this paper, the Riemann–Hilbert problem, with a jump supported on an appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of the corresponding matrix biorthogonal polynomials associated with Laguerre type ...
Amílcar Branquinho +3 more
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Noncommutative Monopoles and Riemann-Hilbert Problems [PDF]
Journal of High Energy Physics, 2004 The Bogomolny equations for Yang-Mills-Higgs monopoles follow from a system of linear equations which may be solved through a parametric Riemann-Hilbert problem. We extend this approach to noncommutative R^3 and use it to (re)construct noncommutative Dirac, Wu-Yang, and BPS monopole configurations in a unified manner.
Lechtenfeld, Olaf, Popov, Alexander D.
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Advances in Difference Equations, 2019 This paper aims to present an application of the Riemann–Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrödinger equation arising in an optical fiber. Starting from the spectral analysis of the
Zhou-Zheng Kang +2 more
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The Baker-Akhiezer function and factorization of the Chebotarev-Khrapkov matrix [PDF]
, 2014 A new technique is proposed for the solution of the Riemann-Hilbert problem with the Chebotarev-Khrapkov matrix coefficient $G(t)=\alpha_1(t)I+\alpha_2(t)Q(t)$, $\alpha_1(t), \alpha_2(t)\in H(L)$, $Q(t)$ is a $2\times 2$ zero-trace polynomial matrix, and
Antipov, Yuri A.
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Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model [PDF]
, 2012 We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model.
Atiyah M. F. +8 more
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Riemann-Hilbert problem, integrability and reductions [PDF]
Journal of Geometric Mechanics, 2019 The present paper is dedicated to integrable models with Mikhailov reduction groups $G_R \simeq \mathbb{D}_h.$ Their Lax representation allows us to prove, that their solution is equivalent to solving Riemann-Hilbert problems, whose contours depend on the realization of the $G_R$-action on the spectral parameter. Two new examples of Nonlinear Evolution
Gerdjikov, Vladimir +2 more
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A coupled complex mKdV equation and its N-soliton solutions via the Riemann–Hilbert approach
Boundary Value Problems, 2023 This paper concerns the initial value problem of a coupled complex mKdV (CCMKDV) equations u t + u x x x + 6 ( | u | 2 + | v | 2 ) u x + 6 u ( | v | 2 ) x = 0 , v t + v x x x + 6 ( | u | 2 + | v | 2 ) v x + 6 v ( | u | 2 ) x = 0 , $$ \begin{aligned} &u_ ...
Siqi Xu
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