Results 1 to 10 of about 502 (136)

Solving the coupled Gerdjikov–Ivanov equation via Riemann–Hilbert approach on the half line [PDF]

Scientific Reports
In this research, the Fokas method is adopted to examine the coupled Gerdjikov–Ivanov equation within the half line interval $$(-\infty ,0]$$ . Meanwhile, the Riemann–Hilbert technique is engaged to work out the potential function associated with the ...
Jiawei Hu, Huanhe Dong, Ning Zhang
doaj   +2 more sources

Riemann–Hilbert boundary value problem for multidimensional elliptic systems of equations

Lietuvos Matematikos Rinkinys, 2023
Multidimensional analogues of Cauchy–Riemann quations and of Riemann–Hilbert boundary value problem are studied. Their relation to the scalar boundary value problem is demonstrated.
Eugenijus Paliokas
doaj   +3 more sources

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
doaj   +1 more source

Riemann–Hilbert Problem for the Matrix Laguerre Biorthogonal Polynomials: The Matrix Discrete Painlevé IV

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, Ana Foulquié Moreno, Assil Fradi, Manuel Mañas   +3 more
doaj   +1 more source

Riemann–Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrödinger equation in an optical fiber

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, Tie-Cheng Xia, Wen-Xiu Ma   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases

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
doaj   +1 more source

A Method of Riemann–Hilbert Problem for Zhang’s Conjecture 1 in a Ferromagnetic 3D Ising Model: Trivialization of Topological Structure

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
doaj   +1 more source

The N-soliton solutions to the M-components nonlinear Schrödinger equations by the Riemann–Hilbert approach

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
doaj   +1 more source