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The piston Riemann problem in a photon superfluid [PDF]
Nature Communications, 2022 The flow of light in nonlinear media can be considered as superfluid flow and described with quantum hydrodynamics. Here the authors demonstrate superfluid flow, optical rarefaction (retracting piston) and shock (pushing piston) wave pairs and ...
Abdelkrim Bendahmane +5 more
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The tacnode Riemann-Hilbert problem [PDF]
Constructive Approximation, 2013 The tacnode Riemann-Hilbert problem is a 4 x 4 matrix valued RH problem that appears in the description of the local behavior of two touching groups of non-intersecting Brownian motions. The same RH problem was also found by Duits and Geudens to describe
Kuijlaars, Arno
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The Riemann problem on a ray for generalized analytic functions with a singular line [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2023 In this paper, we study an inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on a ray for a generalized Cauchy – Riemann equation with a singular coefficient.
Shabalin, Pavel Leonidovich +1 more
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Riemann Problem for a limiting system in elastodynamics
Electronic Journal of Differential Equations, 2014 This article concerns the resolution of the Riemann problem for a 2x2 system in nonconservative form exhibiting parabolic degeneracy. The system can be perceived as the limiting equation (depending on a parameter tending to 0) of a 2x2 strictly ...
Anupam Pal Choudhury
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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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RIEMANN BOUNDARY-VALUE PROBLEM ON CASSINI SPIRALS
Проблемы анализа, 2021 Recently, a number of papers has been published concerning the Riemann boundary-value problems on spiral-like arcs. In all these works, the spiral has the shape close to concentric circles, i. e., with equal rates of torsion in all directions.
L. Zhixin, B. A. Kats
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Riemann-Hilbert problems [PDF]
, 2019 These lectures introduce the method of nonlinear steepest descent for Riemann-Hilbert problems. This method finds use in studying asymptotics associated to a variety of special functions such as the Painlev equations and orthogonal polynomials, in solving the inverse scattering problem for certain integrable systems, and in proving universality for ...
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Results in Physics, 2019 We concern with the Riemann problem for one-dimensional inviscid and isentropic flow of a mixture of a non-ideal gas with small solid particles. The expressions of elementary wave curves are established.
Yicheng Pang +3 more
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The Baker-Akhiezer function and factorization of the Chebotarev-Khrapkov matrix [PDF]
, 2014 A new technique is proposed for the solution of the Riemann-Hilbert problem with the Chebotarev-Khrapkov matrix coefficient $G(t)=\alpha_1(t)I+\alpha_2(t)Q(t)$, $\alpha_1(t), \alpha_2(t)\in H(L)$, $Q(t)$ is a $2\times 2$ zero-trace polynomial matrix, and
Antipov, Yuri A.
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The Perturbed Riemann Problem with Delta Shock for a Hyperbolic System
Advances in Mathematical Physics, 2018 In this paper, we study the perturbed Riemann problem with delta shock for a hyperbolic system. The problem is different from the previous perturbed Riemann problems which have no delta shock.
Xinli Han, Lijun Pan
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