On the Riemann‐Hilbert boundary value problem for generalized analytic functions in the framework of variable exponent spaces
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DOI: 10.1002/mma.4528
Abstract: Let Γ be a simple closed curve that bounds the finite domain D, z=z(ζ)=z(reiϑ) be the conformal mapping of the circle {ζ:|ζ|2andsup0 read more here.
Keywords: riemann hilbert; hilbert boundary; class; value problem ... See more keywords
Riemann‐Hilbert problems and soliton solutions of a multicomponent mKdV system and its reduction
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DOI: 10.1002/mma.5416
Abstract: 1College of Mathematics and Physics, Shanghai University of Electric Power, Shanghai, China 2Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia 3Department of Mathematics and Statistics, University of South Florida, Tampa, Florida 4Department of Mathematics,… read more here.
Keywords: riemann hilbert; mathematics; problems soliton; soliton solutions ... See more keywords
The N‐coupled higher‐order nonlinear Schrödinger equation: Riemann‐Hilbert problem and multi‐soliton solutions
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DOI: 10.1002/mma.6055
Abstract: In this work, the Riemann‐Hilbert (RH) problem of the N‐coupled high‐order nonlinear Schrödinger (N‐CHNLS) equations is studied carefully, which controls the propagation of N fields with all high‐order effects such as high‐order dispersion, self‐steepening effect,… read more here.
Keywords: hilbert problem; order; order nonlinear; problem ... See more keywords
Tau Functions as Widom Constants
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DOI: 10.1007/s00220-018-3230-9
Abstract: We define a tau function for a generic Riemann–Hilbert problem posed on a union of non-intersecting smooth closed curves with jump matrices analytic in their neighborhood. The tau function depends on parameters of the jumps… read more here.
Keywords: riemann hilbert; tau; tau functions; tau function ... See more keywords
Matrix Riemann–Hilbert problems with jumps across Carleson contours
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DOI: 10.1007/s00605-017-1019-0
Abstract: We develop a theory of $$n \times n$$n×n-matrix Riemann–Hilbert problems for a class of jump contours and jump matrices of low regularity. Our basic assumption is that the contour $$\Gamma $$Γ is a finite union… read more here.
Keywords: riemann hilbert; matrix riemann; problems jumps; hilbert ... See more keywords
The Riemann–Hilbert approach to the Helmholtz equation in a quarter-plane: Neumann, Robin and Dirichlet boundary conditions
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DOI: 10.1007/s11005-017-1030-3
Abstract: We revisit the Helmholtz equation in a quarter-plane in the framework of the Riemann–Hilbert approach to linear boundary value problems suggested in late 1990s by A. Fokas. We show the role of the Sommerfeld radiation… read more here.
Keywords: riemann hilbert; equation quarter; helmholtz equation; quarter plane ... See more keywords
Riemann–Hilbert method and multi-soliton solutions of the Kundu-nonlinear Schrödinger equation
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DOI: 10.1007/s11071-020-06102-7
Abstract: In this work, we study the Kundu-nonlinear Schrodinger (Kundu-NLS) equation (so-called the extended NLS equation), which can describe the propagation of the waves in dispersive media. A Lax spectral problem is used to construct the… read more here.
Keywords: riemann hilbert; kundu nonlinear; soliton solutions; solutions kundu ... See more keywords
Riemann-Hilbert problem for a fourth-order dispersive nonlinear Schrödinger equation on the half-line
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2020.124078
Abstract: Abstract In this paper, we investigate a fourth-order dispersive nonlinear Schrodinger equation on the half-line, which has the physical applications in Heisenberg ferromagnetic spin. Solutions for this equation are expressed in form of the unique… read more here.
Keywords: riemann hilbert; order dispersive; half line; dispersive nonlinear ... See more keywords
On compound Riemann Hilbert boundary value problem in the framework of variable exponent spaces
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DOI: 10.1016/j.jmaa.2020.124795
Abstract: Abstract The aim of this paper is to study the compound Riemann Hilbert boundary value problem in the class of Cauchy-type integral with density in variable exponent Lebesgue spaces. The method is transforming the Riemann… read more here.
Keywords: riemann hilbert; value problem; boundary value; hilbert boundary ... See more keywords
Riemann–Hilbert method for the Wadati–Konno–Ichikawa equation: N simple poles and one higher-order pole
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DOI: 10.1016/j.physd.2019.05.008
Abstract: Abstract We present a Riemann–Hilbert (RH) method directly by using the inverse scattering method (ISM) for Wadati–Konno–Ichikawa equation (WKIE) i q t + q 1 + | q | 2 x x = 0 .… read more here.
Keywords: riemann hilbert; order; wadati konno; soliton ... See more keywords
Finite gap integration of the derivative nonlinear Schrödinger equation: A Riemann–Hilbert method
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DOI: 10.1016/j.physd.2019.132213
Abstract: Abstract In this paper we retrieve finite gap solutions of the Gerdjikov–Ivanov type derivative nonlinear Schrodinger equation by using the algebro-geometric method and the Riemann–Hilbert method. We show that the Baker–Akhiezer function of the derivative… read more here.
Keywords: riemann hilbert; derivative nonlinear; method; equation ... See more keywords