Results 11 to 20 of about 11,899 (141)
The inverse scattering transform in the form of a Riemann-Hilbert problem for the Dullin-Gottwald-Holm equation [PDF]
Opuscula Mathematica, 2017 The Cauchy problem for the Dullin-Gottwald-Holm (DGH) equation \[u_t-\alpha^2 u_{xxt}+2\omega u_x +3uu_x+\gamma u_{xxx}=\alpha^2 (2u_x u_{xx} + uu_{xxx})\] with zero boundary conditions (as \(|x|\to\infty\)) is treated by the Riemann-Hilbert approach to
Dmitry Shepelsky, Lech Zielinski
doaj +1 more source
Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
SciPost Physics, 2021 Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz equation arise ...
Yuan Miao, Enej Ilievski, Oleksandr Gamayun
doaj +1 more source
Weyl metrics and Wiener-Hopf factorization
Journal of High Energy Physics, 2020 We consider the Riemann-Hilbert factorization approach to the construction of Weyl metrics in four space-time dimensions. We present, for the first time, a rigorous proof of the remarkable fact that the canonical Wiener-Hopf factorization of a matrix ...
P. Aniceto +3 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
Applied Sciences, 2022 The characterization of electromagnetic metamaterials (MMs) plays a fundamental role in their engineering processes. To this end, the Nicolson–Ross–Weir (NRW) method is intensively used to recover the effective parameters of MMs, even though this is ...
Giovanni Angiulli, Mario Versaci
doaj +1 more source
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
doaj +1 more source
Riemann–Hilbert approach to the elastodynamic equation: half plane
, 2021 We show, how the Riemann–Hilbert approach to the elastodynamic equations, which have been suggested in our preceding papers, works in the half plane case.
Its, Alexander, Its, Elizabeth
core +1 more source
Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval [PDF]
, 2014 We consider polynomials p^w_n(x) that are orthogonal with respect to the oscillatory weight w(x)=exp(iwx) on [?1,1], where w>0 is a real parameter. A first analysis of p^?_n(x) for large values of w was carried out in connection with complex Gaussian ...
Deaño Cabrera, Alfredo, Deaño, Alfredo
core +1 more source
The “Good” Boussinesq Equation: a Riemann-Hilbert Approach
, 2022 We develop an inverse scattering transform formalism for the “good” Boussinesq equation on the line. Assuming that the solution exists, we show that it can be expressed in terms of the solution of a 3 × 3 matrix Riemann-Hilbert problem.
Charlier, Christophe,, Lenells, Jonatan,
core +1 more source
Gravitational effective action at mesoscopic scales from the quantum microstructure of spacetime
Physics Letters B, 2021 At mesoscopic scales, the quantum corrected field equations of gravity should arise from extremising, Ω, the number of microscopic configurations of pre-geometric variables consistent with a given geometry. This Ω, in turn, is the product over all events
T. Padmanabhan
doaj +1 more source