Results 1 to 10 of about 1,080 (97)
Bäcklund-Darboux Transformation for Non-Isospectral Canonical System and Riemann-Hilbert Problem [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 A GBDT version of the Bäcklund-Darboux transformation is constructed for a non-isospectral canonical system, which plays essential role in the theory of random matrix models. The corresponding Riemann-Hilbert problem is treated and some explicit formulas
Alexander Sakhnovich
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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
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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
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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 +3 more
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Long-time asymptotics for the generalized Sasa-Satsuma equation
AIMS Mathematics, 2020 In this paper, we study the long-time asymptotic behavior of the solution of the Cauchy problem for the generalized Sasa-Satsuma equation. Starting with the 3 × 3 Lax pair related to the generalized Sasa-Satsuma equation, we construct a Rieman-Hilbert ...
Kedong Wang +3 more
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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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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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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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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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