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Artículos de revistas sobre el tema "Riemann-Hilbert Probleme"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 1 de febrero de 2022

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1

Kotlyarov, V. P., and E. A. Moskovchenko. "Matrix Riemann-Hilbert Problems and Maxwell-Bloch Equations without Spectral Broadening." Zurnal matematiceskoj fiziki, analiza, geometrii 10, no. 3 (2014): 328–49. http://dx.doi.org/10.15407/mag10.03.328.

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2

Durmagambetov, Asset. "Reduction of modern problems of mathematics to the classical Riemann-Poincare-Hilbert problem." European Journal of Pure and Applied Mathematics 11, no. 4 (2018): 1143–76. http://dx.doi.org/10.29020/nybg.ejpam.v11i4.3328.

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Using the example of a complicated problem such as the Cauchy problem for the Navier--Stokes equation, we show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of solutions for this case. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation, which we consider as a velocity co

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3

Fatykhov, A. Kh, and P. L. Shabalin. "Solvability homogeneous Riemann-Hilbert boundary value problem with several points of turbulence." Issues of Analysis 25 (September 2018): 31–39. http://dx.doi.org/10.15393/j3.art.2018.5530.

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4

Bolibrukh, A. A. "The Riemann-Hilbert problem." Russian Mathematical Surveys 45, no. 2 (1990): 1–58. http://dx.doi.org/10.1070/rm1990v045n02abeh002350.

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5

Kucerovsky, Dan, and Aydin Sarraf. "Solving Riemann-Hilbert problems with meromorphic functions." Acta Universitatis Sapientiae, Mathematica 11, no. 1 (2019): 117–30. http://dx.doi.org/10.2478/ausm-2019-0010.

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Abstract In this paper, we introduce the use of a powerful tool from theoretical complex analysis, the Blaschke product, for the solution of Riemann-Hilbert problems. Classically, Riemann-Hilbert problems are considered for analytic functions. We give a factorization theorem for meromorphic functions over simply connected nonempty proper open subsets of the complex plane and use this theorem to solve Riemann-Hilbert problems where the given data consists of a meromorphic function.

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6

Bertrand, Florian, and Giuseppe Della Sala. "Riemann-Hilbert problems with constraints." Proceedings of the American Mathematical Society 147, no. 5 (2019): 2123–31. http://dx.doi.org/10.1090/proc/14390.

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7

Kuijlaars, Arno. "The Tacnode Riemann–Hilbert Problem." Constructive Approximation 39, no. 1 (2013): 197–222. http://dx.doi.org/10.1007/s00365-013-9225-z.

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8

Filipkovska, M. S., V. P. Kotlyarov, E. A. Melamedova, and E. A. Moskovchenko. "Maxwell-Bloch Equations without Spectral Broadening: Gauge Equivalence, Transformation Operators and Matrix Riemann-Hilbert Problems." Zurnal matematiceskoj fiziki, analiza, geometrii 13, no. 2 (2017): 119–53. http://dx.doi.org/10.15407/mag13.02.119.

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9

Cerne, Miran. "Nonlinear Riemann-Hilbert problem for bordered Riemann surfaces." American Journal of Mathematics 126, no. 1 (2004): 65–87. http://dx.doi.org/10.1353/ajm.2004.0002.

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10

Kamvissis, Spyridon. "A riemann-hilbert problem in a riemann surface." Acta Mathematica Scientia 31, no. 6 (2011): 2233–46. http://dx.doi.org/10.1016/s0252-9602(11)60396-2.

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11

Vyugin, Il'ya V. "Riemann-Hilbert problem for scalar Fuchsian equations and related problems." Russian Mathematical Surveys 66, no. 1 (2011): 35–62. http://dx.doi.org/10.1070/rm2011v066n01abeh004727.

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12

Bojarski, B., and G. Khimshiashvili. "Global Geometric Aspects of Riemann–Hilbert Problems." gmj 8, no. 4 (2001): 713–26. http://dx.doi.org/10.1515/gmj.2001.713.

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Abstract We discuss some global properties of an abstract geometric model for Riemann–Hilbert problems introduced by the first author. In particular, we compute the homotopy groups of elliptic Riemann–Hilbert problems and describe some connections with the theory of Fredholm structures which enable one to introduce more subtle geometrical and topological invariants for families of such problems.

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13

Tao, Mengshuang, and Huanhe Dong. "N-Soliton Solutions of the Coupled Kundu Equations Based on the Riemann-Hilbert Method." Mathematical Problems in Engineering 2019 (March 28, 2019): 1–10. http://dx.doi.org/10.1155/2019/3085367.

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The Kundu equation, which can be used to describe many phenomena in physics and mechanics, has crucial theoretical meaning and research value. In previous studies, the single Kundu equation has been investigated by the Riemann-Hilbert method, but few researchers have focused on the coupled Kundu equations. To our knowledge, many phenomena in nature can be only described by coupled equations, such as species competition and signal interactions. In this paper, we discuss N-soliton solutions of the coupled Kundu equations according to the Riemann-Hilbert method. Starting from the spectral problem

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14

Câmara, M. C., A. F. dos Santos, and Pedro F. dos Santos. "Matrix Riemann–Hilbert problems and factorization on Riemann surfaces." Journal of Functional Analysis 255, no. 1 (2008): 228–54. http://dx.doi.org/10.1016/j.jfa.2008.01.008.

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15

Varzugin, G. G. "Asymptotics of oscillatory Riemann–Hilbert problems." Journal of Mathematical Physics 37, no. 11 (1996): 5869–92. http://dx.doi.org/10.1063/1.531706.

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16

Efendiev, M. A., and W. L. Wendland. "Nonlinear Riemann - Hilbert Problems without Transversality." Mathematische Nachrichten 183, no. 1 (1997): 73–89. http://dx.doi.org/10.1002/mana.19971830106.

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17

Lechtenfeld, Olaf, and Alexander D. Popov. "Noncommutative Monopoles and Riemann-Hilbert Problems." Journal of High Energy Physics 2004, no. 01 (2004): 069. http://dx.doi.org/10.1088/1126-6708/2004/01/069.

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18

Semmler, Gunter, and Elias Wegert. "Separation Principles and Riemann-Hilbert Problems." Computational Methods and Function Theory 2, no. 1 (2003): 175–90. http://dx.doi.org/10.1007/bf03321015.

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19

QIU, W. Y., and R. WONG. "ASYMPTOTIC EXPANSIONS FOR RIEMANN–HILBERT PROBLEMS." Analysis and Applications 06, no. 03 (2008): 269–98. http://dx.doi.org/10.1142/s021953050800116x.

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Let Γ be a piecewise smooth contour in ℂ, which could be unbounded and may have points of self-intersection. Let V(z, N) be a 2 × 2 matrix-valued function defined on Γ, which depends on a parameter N. Consider a Riemann–Hilbert problem for a matrix-valued analytic function R(z, N) that satisfies a jump condition on the contour Γ with the jump matrix V(z, N). Assume that V(z, N) has an asymptotic expansion, as N → ∞, on Γ. An elementary proof is given for the existence of a similar type of asymptotic expansion for the matrix solution R(z, N), as n → ∞, for z ∈ ℂ\Γ. Our method makes use of only

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20

Paliokas, Eugenijus. "MULTIDIMENSIONAL ANALOGUES OF THE RIEMANN–HILBERT BOUNDARY VALUE PROBLEM." Mathematical Modelling and Analysis 12, no. 2 (2007): 205–14. http://dx.doi.org/10.3846/1392-6292.2007.12.205-214.

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21

Zhao, Yi, and Engui Fan. "N-soliton solution for a higher-order Chen–Lee–Liu equation with nonzero boundary conditions." Modern Physics Letters B 34, no. 04 (2019): 2050054. http://dx.doi.org/10.1142/s0217984920500542.

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In this paper, the Riemann–Hilbert approach is applied to investigate a higher-order Chen–Lee–Liu equation with third-order dispersion and quintic nonlinearity terms. Based on the analytical, symmetric and asymptotic properties of eigenfunctions, a generalized Riemann–Hilbert problem associated with Chen–Lee–Liu equation with nonzero boundary conditions is constructed. Further, the [Formula: see text]-soliton solution is found by solving the generalized Riemann–Hilbert problem. As an illustrative example, two kinds of one-soliton solutions with different forms of parameters are obtained.

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22

Röhrl, Helmut. "Book Review: The Riemann-Hilbert problem." Bulletin of the American Mathematical Society 33, no. 02 (1996): 199–203. http://dx.doi.org/10.1090/s0273-0979-96-00646-5.

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23

S. Gerdjikov, Vladimir, Rossen I. Ivanov, and Aleksander A. Stefanov. "Riemann-Hilbert problem, integrability and reductions." Journal of Geometric Mechanics 11, no. 2 (2019): 167–85. http://dx.doi.org/10.3934/jgm.2019009.

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24

Xiao, Zhixing, Kang Li, and Junyi Zhu. "Multiple-Pole Solutions to a Semidiscrete Modified Korteweg-de Vries Equation." Advances in Mathematical Physics 2019 (May 2, 2019): 1–8. http://dx.doi.org/10.1155/2019/5468142.

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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. A different symmetry condition is introduced to build the nonregular Riemann-Hilbert problem. The simplest multiple-pole soliton solution is presented. The dynamics of the solitons are studied.

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25

Ma, Wen-Xiu, Yehui Huang, and Fudong Wang. "Inverse scattering for nonlocal reverse-space multicomponent nonlinear Schrödinger equations." International Journal of Modern Physics B 35, no. 04 (2021): 2150051. http://dx.doi.org/10.1142/s021797922150051x.

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The paper aims to discuss nonlocal reverse-space multicomponent nonlinear Schrödinger equations and their inverse scattering transforms. The inverse scattering problems are analyzed by means of Riemann–Hilbert problems, and Gelfand–Levitan–Marchenko-type integral equations for generalized matrix Jost solutions are determined by the Sokhotski–Plemelj formula. Soliton solutions are generated from the reflectionless transforms associated with zeros of the Riemann–Hilbert problems.

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26

Tyurikov, E. V. "On Some Classes of Correct Problems in the Membrane Theory of Convex Shells." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 3 (207) (October 2, 2020): 25–29. http://dx.doi.org/10.18522/1026-2237-2020-3-25-29.

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On the basis of the theory of the modified Riemann-Hilbert problem for generalized analytic functions, a geometric description is given of a fairly wide family of correct by I. N. Vekua of boundary value problems of the membrane theory of convex hulls with a piecewise smooth boundary. Solutions to the corresponding Riemann-Hilbert problem for an elliptic system of equilibrium equations are found in the classes of N.I. Muskhelishvili and realize a state of tense equilibrium under the condition of stress concentration in corner points. An effective formula is given for calculating the index of t

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27

Basik, A. I., E. V. Hrytsuk, and T. A. Hrytsuk. "The Riemann – Hilbert boundary value problem for elliptic systems of the orthogonal type in R³." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 1 (2020): 7–16. http://dx.doi.org/10.29235/1561-2430-2020-56-1-7-16.

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In this paper, a class of elliptic systems of four 1st order differential equations of the orthogonal type in R3 is considered. For such systems we study the issue of regularizability of the Riemann – Hilbert boundary value problem in an arbitrary limited simply-connected region with a smooth boundary in R3. Using the coefficients of the elliptic system and the matrix of the boundary operator, a special vector field is constructed, and its not entering the tangent plane in any point of the boundary provides the Lopatinski condition of the regularizability of the boundary value problem. The obt

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28

Semmler, Gunter. "Explicit Riemann-Hilbert problems in Hardy spaces." Mathematische Nachrichten 284, no. 8-9 (2011): 1099–117. http://dx.doi.org/10.1002/mana.200710135.

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29

Korotkin, Dmitry, and Vasilisa Shramchenko. "Riemann–Hilbert Problems for Hurwitz Frobenius Manifolds." Letters in Mathematical Physics 96, no. 1-3 (2010): 109–21. http://dx.doi.org/10.1007/s11005-010-0435-z.

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30

dos Santos, António F., and Pedro F. dos Santos. "Lax Equations, Singularities and Riemann–Hilbert Problems." Mathematical Physics, Analysis and Geometry 15, no. 3 (2012): 203–29. http://dx.doi.org/10.1007/s11040-012-9110-1.

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31

Bridgeland, Tom. "Riemann–Hilbert problems from Donaldson–Thomas theory." Inventiones mathematicae 216, no. 1 (2018): 69–124. http://dx.doi.org/10.1007/s00222-018-0843-8.

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32

Semmler, Gunter, and Elias Wegert. "Nonlinear Riemann-Hilbert Problems and Boundary Interpolation." Computational Methods and Function Theory 3, no. 1 (2004): 179–99. http://dx.doi.org/10.1007/bf03321034.

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33

Wegert, Elias, and David Bauer. "On Riemann-Hilbert Problems in Circle Packing." Computational Methods and Function Theory 9, no. 2 (2009): 609–32. http://dx.doi.org/10.1007/bf03321748.

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34

Manjavidze, N. "Riemann–Hilbert Problems on a Cut Plane." Journal of Mathematical Sciences 235, no. 5 (2018): 632–83. http://dx.doi.org/10.1007/s10958-018-4088-2.

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35

Zhou, Xin. "The Riemann–Hilbert Problem and Inverse Scattering." SIAM Journal on Mathematical Analysis 20, no. 4 (1989): 966–86. http://dx.doi.org/10.1137/0520065.

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36

Greenberg, W., P. F. Zweifel, and S. Paveri‐Fontana. "The Riemann–Hilbert problem for nonsymmetric systems." Journal of Mathematical Physics 32, no. 12 (1991): 3540–45. http://dx.doi.org/10.1063/1.529415.

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37

Arciga-Alejandre, M. P., J. Sanchez-Ortiz, and M. A. Taneco-Hernandez. "Asymptotic for a Riemann-Hilbert problem solution." International Journal of Mathematical Analysis 7 (2013): 1667–72. http://dx.doi.org/10.12988/ijma.2013.3358.

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38

Kapaev, Andrei A. "Riemann Hilbert problem for bi-orthogonal polynomials." Journal of Physics A: Mathematical and General 36, no. 16 (2003): 4629–40. http://dx.doi.org/10.1088/0305-4470/36/16/312.

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39

Giorgadze, G., and G. Khimshiashvili. "The Riemann-Hilbert problem in loop spaces." Doklady Mathematics 73, no. 2 (2006): 258–60. http://dx.doi.org/10.1134/s1064562406020281.

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40

Kuijlaars, A. B. J., and K. T. R. McLaughlin. "A Riemann–Hilbert problem for biorthogonal polynomials." Journal of Computational and Applied Mathematics 178, no. 1-2 (2005): 313–20. http://dx.doi.org/10.1016/j.cam.2004.01.043.

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41

Branquinho, A., U. Fidalgo, and A. Foulquié Moreno. "Riemann–Hilbert problem associated with Angelesco systems." Journal of Computational and Applied Mathematics 233, no. 3 (2009): 643–51. http://dx.doi.org/10.1016/j.cam.2009.02.032.

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42

Llewellyn Smith, Stefan G., and Elena Luca. "Numerical solution of scattering problems using a Riemann–Hilbert formulation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2229 (2019): 20190105. http://dx.doi.org/10.1098/rspa.2019.0105.

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A fast and accurate numerical method for the solution of scalar and matrix Wiener–Hopf (WH) problems is presented. The WH problems are formulated as Riemann–Hilbert problems on the real line, and a numerical approach developed for these problems is used. It is shown that the known far-field behaviour of the solutions can be exploited to construct numerical schemes providing spectrally accurate results. A number of scalar and matrix WH problems that generalize the classical Sommerfeld problem of diffraction of plane waves by a semi-infinite plane are solved using the approach.

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43

Antipov, Y. A. "Vector Riemann–Hilbert problem with almost periodic and meromorphic coefficients and applications." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2180 (2015): 20150262. http://dx.doi.org/10.1098/rspa.2015.0262.

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The vector Riemann–Hilbert problem is analysed when the entries of its matrix coefficient are meromorphic and almost periodic functions. Three cases for the meromorphic functions, when they have (i) a finite number of poles and zeros (rational functions), (ii) periodic poles and zeros, and (iii) an infinite number of non-periodic zeros and poles, are considered. The first case is illustrated by the heat equation for a composite rod with a finite number of discontinuities and a system of convolution equations; both problems are solved explicitly. In the second case, a Wiener–Hopf factorization

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44

Ling, Liming, and Wen-Xiu Ma. "Inverse Scattering and Soliton Solutions of Nonlocal Complex Reverse-Spacetime Modified Korteweg-de Vries Hierarchies." Symmetry 13, no. 3 (2021): 512. http://dx.doi.org/10.3390/sym13030512.

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This paper aims to explore nonlocal complex reverse-spacetime modified Korteweg-de Vries (mKdV) hierarchies via nonlocal symmetry reductions of matrix spectral problems and to construct their soliton solutions by the inverse scattering transforms. The corresponding inverse scattering problems are formulated by building the associated Riemann-Hilbert problems. A formulation of solutions to specific Riemann-Hilbert problems, with the jump matrix being the identity matrix, is established, where eigenvalues could equal adjoint eigenvalues, and thus N-soliton solutions to the nonlocal complex rever

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45

Devadze, David. "The Existence of a Generalized Solution of an m-Point Nonlocal Boundary Value Problem." Communications in Mathematics 25, no. 2 (2017): 159–69. http://dx.doi.org/10.1515/cm-2017-0013.

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Abstract An m-point nonlocal boundary value problem is posed for quasi- linear differential equations of first order on the plane. Nonlocal boundary value problems are investigated using the algorithm of reducing nonlocal boundary value problems to a sequence of Riemann-Hilbert problems for a generalized analytic function. The conditions for the existence and uniqueness of a generalized solution in the space are considered.

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46

Li, Xin Gang, Nian Chun Lü, Guo Zhi Song, and Cheng Jin. "Dislocation Distribution Function of the Surfaces of Mode III Dynamic Crack Subjected to Unit-Step Loads and Moving Increasing Loads." Key Engineering Materials 324-325 (November 2006): 101–4. http://dx.doi.org/10.4028/www.scientific.net/kem.324-325.101.

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By the theory of complex functions, dislocation distribution function concerning mode dynamic crack propagation problem under the conditions of unit-step loads and moving increasing loads was studied respectively. Analytical solution representations are attained by the methods of self-similar functions. The problems investigated can be transformed into Riemann-Hilbert problems and their closed solutions are obtained rather simple by this approach.

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47

Luan, Xu, Nian Chun Lü, and Cheng Jin. "Solution of the Edges of Mode III Asymmetrical Dynamic Interface Crack Subjected to Variable Loads." Key Engineering Materials 419-420 (October 2009): 709–12. http://dx.doi.org/10.4028/www.scientific.net/kem.419-420.709.

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By the approaches of the theory of complex functions, propagation problems concerning mode Ⅲ asymmetrical dynamic interface crack were studied. The problems can be transformed into Riemann-Hilbert problem easily by the measures of self-similar functions, and the universal expressions of analytical solutions of the edges of mode Ⅲ asymmetrical dynamics interface crack subjected to variable loads and respectively, were attained.

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48

Shanin, A. V., and A. I. Korolkov. "Diffraction by an impedance strip I. Reducing diffraction problem to Riemann–Hilbert problems." Quarterly Journal of Mechanics and Applied Mathematics 68, no. 3 (2015): 321–39. http://dx.doi.org/10.1093/qjmam/hbv010.

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49

Câmara, M. C., and M. T. Malheiro. "Factorization in a torus and Riemann–Hilbert problems." Journal of Mathematical Analysis and Applications 386, no. 1 (2012): 343–63. http://dx.doi.org/10.1016/j.jmaa.2011.08.002.

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50

Bastos, M. A., Yu I. Karlovich, and A. F. dos Santos. "Oscillatory Riemann–Hilbert problems and the corona theorem." Journal of Functional Analysis 197, no. 2 (2003): 347–97. http://dx.doi.org/10.1016/s0022-1236(03)00007-7.

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