Results 1 to 10 of about 357 (99)

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

Nonlocal PT-symmetric integrable equations and related Riemann–Hilbert problems

Partial Differential Equations in Applied Mathematics, 2021
We aim to discuss about how to construct and classify nonlocal PT-symmetric integrable equations via nonlocal group reductions of matrix spectral problems.
Wen-Xiu Ma
doaj   +1 more source

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

Riemann–Hilbert Problems and Soliton Solutions of Type (${\lambda }^{\ast }$, $-{\lambda }^{\ast }$) Reduced Nonlocal Integrable mKdV Hierarchies

Mathematics, 2022
Reduced nonlocal matrix integrable modified Korteweg–de Vries (mKdV) hierarchies are presented via taking two transpose-type group reductions in the matrix Ablowitz–Kaup–Newell–Segur (AKNS) spectral problems.
Wen-Xiu Ma
doaj   +1 more source

Soliton hierarchies and soliton solutions of type (−λ∗, −λ) reduced nonlocal nonlinear Schrödinger equations of arbitrary even order

Partial Differential Equations in Applied Mathematics, 2023
We present mixed-type reduced soliton hierarchies of nonlocal integrable nonlinear Schrödinger equations of arbitrary even order by conducting two nonlocal group reductions for the Ablowitz–Kaup–Newell–Segur matrix spectral problems.
Wen-Xiu Ma
doaj   +1 more source

The solvability of a kind of generalized Riemann–Hilbert problems on function spaces H ∗ $H_{\ast }$

Journal of Inequalities and Applications, 2020
In this paper, we study a kind of generalized Riemann–Hilbert problems (R-HPs) with several unknown functions in strip domains. We mainly discuss methods of solving R-HPs with two unknown functions and obtain general solutions and conditions of ...
Pingrun Li
doaj   +1 more source

Riemann–Hilbert problems with shift on the Lyapunov curve for null-solutions of iterated Beltrami equations

Boundary Value Problems, 2019
In this article, we study some Riemann–Hilbert problems with shift on the Lyapunov curve for generalized polyanalytic functions, which are null-solutions of a class of iterated Beltrami equations.
Guoan Guo, Chenkai Jin, Pei Dang, Zhihua Du   +3 more
doaj   +1 more source

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
doaj   +1 more source

A Riemann-Hilbert Approach to the Multicomponent Kaup-Newell Equation

Advances in Mathematical Physics, 2020
A Riemann-Hilbert approach is developed to the multicomponent Kaup-Newell equation. The formula is presented of N-soliton solutions through an identity jump matrix related to the inverse scattering problems with reflectionless potential.
Jian-bing Zhang, Ze-xuan Zhang
doaj   +1 more source

TBA equations and resurgent Quantum Mechanics

Journal of High Energy Physics, 2019
We derive a system of TBA equations governing the exact WKB periods in one-dimensional Quantum Mechanics with arbitrary polynomial potentials. These equations provide a generalization of the ODE/IM correspondence, and they can be regarded as the solution
Katsushi Ito, Marcos Mariño, Hongfei Shu   +2 more
doaj   +1 more source