2001, Progress in nonlinear differential equations and their applications, ISBN 0817640800, Volume 38, xv, 317

Book

2008, CBMS-NSF regional conference series in applied mathematics, ISBN 9780898716511, Volume 78, xv, 336

Book

Journal of Differential Equations, ISSN 0022-0396, 01/2017, Volume 262, Issue 1, pp. 506 - 558

Boundary value problems for integrable nonlinear differential equations can be analyzed via the Fokas method. In this paper, this method is employed in order...

Integrable system | Initial–boundary value problem | Dirichlet-to-Neumann map | Riemann–Hilbert problem | Coupled nonlinear Schrödinger equation | MKDV EQUATION | INTEGRABILITY | CAMASSA-HOLM EQUATION | LONG-TIME ASYMPTOTICS | SINE-GORDON EQUATION | EVOLUTION-EQUATIONS | MATHEMATICS | Riemann-Hilbert problem | Coupled nonlinear Schrodinger equation | SOLITONS | HALF-LINE | Initial-boundary value problem | X-3 LAX PAIRS | Analysis | Methods | Differential equations

Integrable system | Initial–boundary value problem | Dirichlet-to-Neumann map | Riemann–Hilbert problem | Coupled nonlinear Schrödinger equation | MKDV EQUATION | INTEGRABILITY | CAMASSA-HOLM EQUATION | LONG-TIME ASYMPTOTICS | SINE-GORDON EQUATION | EVOLUTION-EQUATIONS | MATHEMATICS | Riemann-Hilbert problem | Coupled nonlinear Schrodinger equation | SOLITONS | HALF-LINE | Initial-boundary value problem | X-3 LAX PAIRS | Analysis | Methods | Differential equations

Journal Article

2016, Graduate studies in mathematics, ISBN 9780821848418, Volume 172, xi, 461

Random matrices (probabilistic aspects; for algebraic aspects see 15B52) | Equations of mathematical physics and other areas of application | Partial differential equations | Approximations and expansions | Probability theory and stochastic processes | Special matrices | Operator theory | Probability theory on algebraic and topological structures | Riemann-Hilbert problems | Exact enumeration problems, generating functions | Convex and discrete geometry | Special classes of linear operators | Combinatorics | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) | Time-dependent statistical mechanics (dynamic and nonequilibrium) | Enumerative combinatorics | Exactly solvable dynamic models | Linear and multilinear algebra; matrix theory | Special processes | Statistical mechanics, structure of matter | Toeplitz operators, Hankel operators, Wiener-Hopf operators | Tilings in $2$ dimensions | Interacting random processes; statistical mechanics type models; percolation theory | Discrete geometry | Random matrices | Combinatorial analysis

Book

2003, Cambridge monographs on applied and computational mathematics, ISBN 0521772966, Volume 11, xvi, 349

Numerical simulation of compressible, inviscid time-dependent flow is a major branch of computational fluid dynamics. Its primary goal is to obtain accurate...

Fluid dynamics | Riemann-Hilbert problems

Fluid dynamics | Riemann-Hilbert problems

Book

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2017, Volume 50, Issue 39, p. 395204

In this paper, we implement the Fokas method in order to study initial boundary value problems of the coupled modified Korteweg-de Vries equation formulated on...

Riemann-Hilbert problem | integrable system | initial-boundary value problem | Dirichlet to Neumann map | coupled modified Korteweg-de Vries equation | INTERVAL | PHYSICS, MULTIDISCIPLINARY | DEVRIES EQUATION | MODIFIED KDV EQUATIONS | SINE-GORDON EQUATION | PDES | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | UNIFIED TRANSFORM METHOD | X-3 LAX PAIRS

Riemann-Hilbert problem | integrable system | initial-boundary value problem | Dirichlet to Neumann map | coupled modified Korteweg-de Vries equation | INTERVAL | PHYSICS, MULTIDISCIPLINARY | DEVRIES EQUATION | MODIFIED KDV EQUATIONS | SINE-GORDON EQUATION | PDES | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | UNIFIED TRANSFORM METHOD | X-3 LAX PAIRS

Journal Article

Journal of Geometry and Physics, ISSN 0393-0440, 10/2018, Volume 132, pp. 45 - 54

A 3 3 matrix spectral problem is introduced and its associated AKNS integrable hierarchy with four components is generated. From this spectral problem, a...

[formula omitted]-soliton solution | Riemann–Hilbert problem | Integrable hierarchy | N-soliton solution | MATHEMATICS | Riemann-Hilbert problem | INTEGRABLE SYSTEMS | EQUATIONS | HAMILTONIAN STRUCTURES | SEMIDIRECT SUMS | PHYSICS, MATHEMATICAL | HIERARCHY

[formula omitted]-soliton solution | Riemann–Hilbert problem | Integrable hierarchy | N-soliton solution | MATHEMATICS | Riemann-Hilbert problem | INTEGRABLE SYSTEMS | EQUATIONS | HAMILTONIAN STRUCTURES | SEMIDIRECT SUMS | PHYSICS, MATHEMATICAL | HIERARCHY

Journal Article

Lecture Notes in Mathematics, ISSN 0075-8434, 2016, Volume 2153, pp. 75 - 86

Journal Article

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, ISSN 1364-5021, 09/2019, Volume 475, Issue 2229, p. 20190105

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 | Wiener-Hopf | Sommerfeld | WIENER-HOPF FACTORIZATION | scattering | BOUNDARY-VALUE PROBLEM | PLANE | MULTIDISCIPLINARY SCIENCES | DIFFRACTION

Riemann-Hilbert | Wiener-Hopf | Sommerfeld | WIENER-HOPF FACTORIZATION | scattering | BOUNDARY-VALUE PROBLEM | PLANE | MULTIDISCIPLINARY SCIENCES | DIFFRACTION

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 02/2018, Volume 364, pp. 27 - 61

We employ the Ablowitz–Ladik system as an illustrative example in order to demonstrate how to analyze initial–boundary value problems for integrable nonlinear...

Integrable system | Initial–boundary value problem | Riemann–Hilbert problem | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PDES | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | Riemann-Hilbert problem | HALF-LINE | Initial-boundary value problem | DIRICHLET | DIFFERENTIAL-DIFFERENCE EQUATIONS | X-3 LAX PAIRS | HIERARCHY | Physics - Exactly Solvable and Integrable Systems

Integrable system | Initial–boundary value problem | Riemann–Hilbert problem | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | PDES | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | Riemann-Hilbert problem | HALF-LINE | Initial-boundary value problem | DIRICHLET | DIFFERENTIAL-DIFFERENCE EQUATIONS | X-3 LAX PAIRS | HIERARCHY | Physics - Exactly Solvable and Integrable Systems

Journal Article

1995, Proceedings of the Steklov Institute of Mathematics, ISBN 0821804669, Volume 206., viii, 145

Book

2016, Graduate studies in mathematics, ISBN 1470430959, Volume 177, xxiii, 275 pages

Book

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 2, pp. 797 - 816

In this paper a theory is developed for obtaining families of solutions to the KdV equation by formulating a Riemann–Hilbert problem with an appropriate shift....

Factorization | Integrable systems | Riemann–Hilbert problems | Riemann-Hilbert problems | MATHEMATICS | MATHEMATICS, APPLIED | DE-VRIES EQUATION | Analysis | Numerical analysis

Factorization | Integrable systems | Riemann–Hilbert problems | Riemann-Hilbert problems | MATHEMATICS | MATHEMATICS, APPLIED | DE-VRIES EQUATION | Analysis | Numerical analysis

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 01/2020, Volume 364, p. 124686

In this paper, we establish some properties of the Hilbert transform in Clifford analysis setting, and mainly show the weak type (1,1) inequality for the...

Hilbert transform | Fourier transform | Dirac operator | Calderón–Zygmund decomposition | Riemann–Hilbert problems | MATHEMATICS, APPLIED | Riemann-Hilbert problems | Calderon-Zygmund decomposition

Hilbert transform | Fourier transform | Dirac operator | Calderón–Zygmund decomposition | Riemann–Hilbert problems | MATHEMATICS, APPLIED | Riemann-Hilbert problems | Calderon-Zygmund decomposition

Journal Article

16.
Initial-boundary value problems for the coupled modified korteweg-de vries equation on the interval

Communications on Pure and Applied Analysis, ISSN 1534-0392, 05/2018, Volume 17, Issue 3, pp. 923 - 957

In this paper, we study the initial-boundary value problems of the coupled modified Korteweg-de Vries equation formulated on the finite interval with Lax pairs...

Integrable system | Initial-boundary value problem | Riemann-hilbert problem | MATHEMATICS, APPLIED | DEVRIES EQUATION | MODIFIED KDV EQUATIONS | PDES | EVOLUTION-EQUATIONS | initial-boundary value problem | NONLINEAR SCHRODINGER-EQUATION | MATHEMATICS | Riemann-Hilbert problem | HALF-LINE | TRANSFORM | X-3 LAX PAIRS

Integrable system | Initial-boundary value problem | Riemann-hilbert problem | MATHEMATICS, APPLIED | DEVRIES EQUATION | MODIFIED KDV EQUATIONS | PDES | EVOLUTION-EQUATIONS | initial-boundary value problem | NONLINEAR SCHRODINGER-EQUATION | MATHEMATICS | Riemann-Hilbert problem | HALF-LINE | TRANSFORM | X-3 LAX PAIRS

Journal Article

1996, Pitman monographs and surveys in pure and applied mathematics, ISBN 0582292042, Volume 80, 269

Book

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2016, Volume 307, pp. 248 - 261

Riemann–Hilbert problems in multiply connected domains arise in a number of applications, such as the computation of conformal maps. As an example here, we...

Multiply connected domains | Conformal mapping | Riemann–Hilbert problems | MATHEMATICS, APPLIED | Riemann-Hilbert problems | Linear systems | Maps | Computation | Exteriors | Disks | Mathematical models | Slits | Inclination

Multiply connected domains | Conformal mapping | Riemann–Hilbert problems | MATHEMATICS, APPLIED | Riemann-Hilbert problems | Linear systems | Maps | Computation | Exteriors | Disks | Mathematical models | Slits | Inclination

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 09/2018, Volume 332, pp. 148 - 159

In this work, we investigate the two-component modified Korteweg-de Vries (mKdV) equation, which is a complete integrable system, and accepts a generalization...

Initial-boundary value problem | Unified transform method | Two-component mKdV equation | Riemann–Hilbert problem | MATHEMATICS, APPLIED | Riemann-Hilbert problem | SOLITON-SOLUTIONS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | KDV

Initial-boundary value problem | Unified transform method | Two-component mKdV equation | Riemann–Hilbert problem | MATHEMATICS, APPLIED | Riemann-Hilbert problem | SOLITON-SOLUTIONS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | KDV

Journal Article

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, ISSN 1815-0659, 2019, Volume 15

In this paper some open problems for Painleve equations are discussed. In particular the following open problems are described: (i) the Painleve equivalence...

open problems | POLYNOMIAL HAMILTONIANS | SIMILARITY REDUCTIONS | LARGE-DEGREE ASYMPTOTICS | PHYSICS, MATHEMATICAL | Painleve equations | UNITARY-MATRIX MODELS | NUMERICAL-SOLUTION | 2ND-ORDER ODES | EQUIVALENCE PROBLEM | RIEMANN-HILBERT PROBLEMS | NONLINEAR EVOLUTION-EQUATIONS | ORDINARY DIFFERENTIAL-EQUATIONS

open problems | POLYNOMIAL HAMILTONIANS | SIMILARITY REDUCTIONS | LARGE-DEGREE ASYMPTOTICS | PHYSICS, MATHEMATICAL | Painleve equations | UNITARY-MATRIX MODELS | NUMERICAL-SOLUTION | 2ND-ORDER ODES | EQUIVALENCE PROBLEM | RIEMANN-HILBERT PROBLEMS | NONLINEAR EVOLUTION-EQUATIONS | ORDINARY DIFFERENTIAL-EQUATIONS

Journal Article

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