Results 11 to 20 of about 14,965,840 (158)

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
doaj   +2 more sources

Dynamical Behavior Analysis of Generalized Chen–Lee–Liu Equation via the Riemann–Hilbert Approach

Fractal and Fractional
In this paper, we investigate the dynamics of the generalized Chen–Lee–Liu (gCLL) equation utilizing the Riemann–Hilbert method to derive its N-soliton solution.
Wenxia Chen, Chaosheng Zhang, Lixin Tian
doaj   +2 more sources

Mixed single, double, and triple poles solutions for the space-time shifted nonlocal DNLS equation with nonzero boundary conditions via Riemann–Hilbert approach

Nuclear Physics B
In this paper, we investigate the space-time shifted nonlocal derivative nonlinear Schrödinger (DNLS) equation under nonzero boundary conditions using the Riemann–Hilbert (RH) approach for the first time.
Xin-Yu Liu, Rui Guo
doaj   +2 more sources

Direct and inverse scattering problems of the modified Sawada–Kotera equation: Riemann–Hilbert approach

Proceedings of the Royal Society A, 2022
It is known that both the Sawada–Kotera equation and the Kaup–Kupershmidt equation are related with the same modified equation by different Miura transformations.
Deng Wang, Xiaodong Zhu
semanticscholar   +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 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

The transition between the gap probabilities from the Pearcey to the Airy process; a Riemann-Hilbert approach [PDF]

, 2011
We consider the gap probability for the Pearcey and Airy processes; we set up a Riemann--Hilbert approach (different from the standard one) whereby the asymptotic analysis for large gap/large time of the Pearcey process is shown to factorize into two ...
Adler, Adler, Adler, Adler, Adler, Baik, Bergere, Bertola, Bleher, Bleher, Borodin, Borodin, Bowick, Brézin, Deift, Deift, Ferrari, Fokas, Harnad, Harnad, Hastings, Its, Jimbo, Jimbo, Jimbo, Johansson, M. Bertola, M. Cafasso, Malgrange, Mehta, Moore, Okounkov, Tracy, Tracy, Tracy   +34 more
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A Riemann-Hilbert approach to rotating attractors

Journal of High Energy Physics, 2017
We construct rotating extremal black hole and attractor solutions in gravity theories by solving a Riemann-Hilbert problem associated with the Breitenlohner-Maison linear system. By employing a vectorial Riemann-Hilbert factorization method we explicitly
M. C. Câmara, G. L. Cardoso, T. Mohaupt, S. Nampuri   +3 more
doaj   +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

The existence of a real pole-free solution of the fourth order analogue of the Painleve I equation [PDF]

, 2006
We establish the existence of a real solution y(x,T) with no poles on the real line of the following fourth order analogue of the Painleve I equation, x=Ty-({1/6}y^3+{1/24}(y_x^2+2yy_{xx})+{1/240}y_{xxxx}).
Claeys T, Claeys T, Deift P, Deift P, Fokas A S, Grava T, Its A R, Kapaev A A, Kawai T, Kudryashov N A Efimova O Y, Lax P D, Lax P D, Lax P D, M Vanlessen, Reed M, T Claeys, Venakides S   +16 more
core   +1 more source