Results 11 to 20 of about 1,446 (167)

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
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Semiclassical limit of the focusing NLS: Whitham equations and the Riemann–Hilbert Problem approach [PDF]

Physica D: Nonlinear Phenomena, 2016
The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated $N$-phase nonlinear wave solutions to the focusing nonlinear Schr dinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated $N ...
Tovbis, Alexander, El, Gennady A.
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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
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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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Quantum periods and TBA equations for N=2 SU(2) Nf = 2 SQCD with flavor symmetry

Physics Letters B, 2021
We apply the exact WKB analysis to the quantum Seiberg-Witten curve for 4-dimensional N=2 SU(2) Nf=2 SQCD with the flavor symmetry. The discontinuity and the asymptotic behavior of the quantum periods define a Riemann-Hilbert problem.
Keita Imaizumi
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The Prolongation Structure of the Modified Nonlinear Schrödinger Equation and Its Initial-Boundary Value Problem on the Half Line via the Riemann-Hilbert Approach

Mathematics, 2019
In this paper, the Lax pair of the modified nonlinear Schrödinger equation (mNLS) is derived by means of the prolongation structure theory. Based on the obtained Lax pair, the mNLS equation on the half line is analyzed with the assistance of Fokas ...
Tongshuai Liu, Huanhe Dong
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The N-soliton solutions of the n-component generalized Sasa-Satsuma system: Riemann-Hilbert method

Nuclear Physics B
Using the Riemann-Hilbert method, the paper systematically investigates the n-component generalized Sasa-Satsuma system. By utilizing the Tu scheme, we systematically construct the n-component generalized Sasa-Satsuma integrable hierarchy, and obtain the
Zhiguo Ren, Jing Yu, Lin Huang
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Multidimensional analogues of the Riemann–Hilbert boundary value problem

Mathematical Modelling and Analysis, 2007
Multidimensional generalizations of the Cauchy‐Riemann systems and two different types of analogues of the Riemann–Hilbert boundary value problems for these systems are considered.
Eugenijus Paliokas
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Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation

Advanced Nonlinear Studies
Resorting to the spectral analysis of the 4 × 4 matrix spectral problem, we construct a 4 × 4 matrix Riemann–Hilbert problem to solve the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation.
Chen Mingming, Geng Xianguo, Liu Huan
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A Riemann–Hilbert approach to solution of the modified focusing complex short pulse equation

Frontiers in Applied Mathematics and Statistics
We develop a Riemann–Hilbert approach to the modified focusing complex short pulse (mfcSP) equationuxt=u+12u¯(u2)xxwith zero boundary conditions (as |x| → ∞).
Ruslan Barkov, Dmitry Shepelsky, Dmitry Shepelsky   +2 more
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