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Nonlinear Riemann-Hilbert Problems

, 2004
Gunter Semmler
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The Riemann-Hilbert Problem and the Generalized Neumann Kernel on Un-Bounded Multiply Connected Regions

Mohamed M. S. Nasser
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A Spectral–Topological Program toward the Riemann Hypothesis in the Spirit of the Hilbert–Pólya Method_OMG! Unconditional Resolution of the Inverse Spectral Problem

Karadzhov, Tosho Lazarov
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The Riemann-Hilbert Problem

Notices of the International Consortium of Chinese Mathematicians
having singularities at points a1, . . . , am; that is, suppose that the bij(z)’s are holomorphic functions on P \ {a1, . . . , am}. Locally, such a system always admit a solution, but global solutions are multi-valued in general.
Gabriel Chênevert, Eyal Z. Goren
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The Riemann-Hilbert problem

Russian Mathematical Surveys, 1990
A. Bolibrukh
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Riemann–Hilbert problem and interactions of solitons in the n$n$ ‐component nonlinear Schrödinger equations

Studies in applied mathematics (Cambridge), 2021
In this work, we systematically investigate the general n$n$ ‐component nonlinear Schrödinger equations by using the Riemann–Hilbert method. Starting from the Lax pair associated with an (n+1)×(n+1)$(n + 1)\times (n + 1)$ matrix spectral problem, we ...
Yuan Li, Shou‐Fu Tian, Jin-Jie Yang
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General N-soliton solutions to the two types of nonlocal Gerdjikov-Ivanov equations via Riemann-Hilbert problem

Physica Scripta, 2023
This paper mainly makes use of the Riemann-Hilbert approach to solve the two types of nonlocal Gerdjikov-Ivanov equations derived by different nonlocal group reductions.
Yingmin Yang, T. Xia, Tongshuai Liu
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Renormalization in Quantum Field Theory and the Riemann–Hilbert Problem I: The Hopf Algebra Structure of Graphs and the Main Theorem

, 1999
:This paper gives a complete selfcontained proof of our result announced in [6] showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on the Riemann–Hilbert ...
A. Connes, D. Kreimer
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H-polarized plane-wave scattering by a PEC strip grating on top of a dielectric substrate: analytical regularization based on the Riemann-Hilbert Problem solution

, 2020
We consider the H-polarized plane wave scattering from an infinite flat grating of perfectly electrically conducting strips, placed on the interface of a dielectric slab.
Fedir O. Yevtushenko, S. Dukhopelnykov, A. Nosich   +2 more
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The N‐coupled higher‐order nonlinear Schrödinger equation: Riemann‐Hilbert problem and multi‐soliton solutions

Mathematical methods in the applied sciences, 2019
In this work, the Riemann‐Hilbert (RH) problem of the N‐coupled high‐order nonlinear Schrödinger (N‐CHNLS) equations is studied carefully, which controls the propagation of N fields with all high‐order effects such as high‐order dispersion, self ...
Jin-Jie Yang, Shou‐Fu Tian, Wei-Qi Peng, Tian‐Tian Zhang   +3 more
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