Results 31 to 40 of about 17,890 (258)
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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On the origins of Riemann–Hilbert problems in mathematics* [PDF]
Nonlinearity, 2021 Abstract This article is firstly a historic review of the theory of Riemann–Hilbert problems with particular emphasis placed on their original appearance in the context of Hilbert’s 21st problem and Plemelj’s work associated with it. The secondary purpose of this note is to invite a new generation of mathematicians to the fascinating ...
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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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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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Riemann–Hilbert problem and matrix biorthogonal polynomials [PDF]
, 2021 Recently the Riemann-Hilbert problem, with jumps supported on appropriate curves in the complex plane, has been presented for matrix biorthogonal polynomials, in particular non-Abelian Hermite matrix biorthogonal polynomials in the real line ...
Amílcar Branquinho +5 more
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Multiple-Pole Solutions to a Semidiscrete Modified Korteweg-de Vries Equation
Advances in Mathematical Physics, 2019 Multiple-pole soliton solutions to a semidiscrete modified Korteweg-de Vries equation are derived by virtue of the Riemann-Hilbert problem with higher-order zeros.
Zhixing Xiao, Kang Li, Junyi Zhu
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Mathematics, 2021 A method of the Riemann–Hilbert problem is employed for Zhang’s conjecture 2 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in a zero external magnetic field.
Zhidong Zhang, Osamu Suzuki
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Mathematics, 2021 A method of the Riemann–Hilbert problem is applied for Zhang’s conjecture 1 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in the zero external field and the solution to the Zhang’s conjecture 1 is ...
Osamu Suzuki, Zhidong Zhang
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The nonlinear Schr\"odinger equation with forcing involving products of eigenfunctions [PDF]
Open Communications in Nonlinear Mathematical Physics, 2022 We elaborate on a new methodology, which starting with an integrable evolution equation in one spatial dimension, constructs an integrable forced version of this equation.
A. S. Fokas, A. Latifi
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Partial Differential Equations in Applied Mathematics, 2022 In this paper, the main work is to study the N-soliton solutions for the M-component nonlinear Schrödinger equations, the matrix Riemann–Hilbert problem is constructed for this integrable hierarchies by analyzing the block matrix spectral problem of the ...
Jian Li, Tiecheng Xia
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