Inverse scattering on the half-line for ZS-AKNS systems with integrable potentials

DOI10.1007/s00020-015-2269-7zbMath1347.34129OpenAlexW2254109378WikidataQ59472949 ScholiaQ59472949MaRDI QIDQ279701

Rostyslav O. Hryniv, Stepan S. Manko

Publication date: 29 April 2016

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-015-2269-7

zbMATH Keywords

inverse scatteringMarchenko equationscattering function, Jost functionZS-AKNS systems

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Inverse scattering problems in quantum theory (81U40) (S)-matrix theory, etc. in quantum theory (81U20) Inverse problems involving ordinary differential equations (34A55) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (8)

Resonances for the Dirac operator on the half-line ⋮ Inverse scattering on the half-line for generalized ZS-AKNS system with general boundary conditions ⋮ Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions ⋮ Inverse scattering on the half-line for a first-order system with a general boundary condition ⋮ Stability of resonances for the Dirac operator ⋮ Inverse resonance scattering for massless Dirac operators on the real line ⋮ Inverse scattering on the half-line for energy-dependent Schrödinger equations ⋮ Inverse resonance scattering for Dirac operators on the half-line

Cites Work

• Characterization of scattering data for the AKNS system
• On an inverse scattering problem for a class of Dirac operators with spectral parameter in the boundary condition
• The Kolmogorov-Riesz compactness theorem
• Energy dependent inverse scattering on the line
• Spectral theory of the Klein-Gordon equation in Pontryagin spaces
• Scattering operators for matrix Zakharov-Shabat systems
• Spectral theory of ordinary differential operators
• On the inverse scattering problem for the one-dimensional Schrödinger equation with an energy dependent potential
• Inverse-scattering problem for a system of differential equations
• Inverse scattering up to smooth functions for the Dirac-ZS-AKNS system
• On the deficiency indices and self-adjointness of symmetric Hamiltonian systems
• Energy dependent scattering theory
• Scattering of solitons for Dirac equation coupled to a particle
• Inverse eigenvalue problem for a vibration of a string with viscous drag
• Inverse scattering for a Schrödinger equation with energy dependent potential
• On an inverse scattering problem for a class Dirac operator with discontinuous coefficient and nonlinear dependence on the spectral parameter in the boundary condition
• Inverse Scattering for Schrödinger Operators with Miura Potentials, II. Different Riccati Representatives
• Eigenvalues of the Klein-Gordon equation
• On the Jost solutions of the Schrödinger-type equations with a polynomial energy-dependent potential
• Inverse scattering problem for the Schrödinger-type equation with a polynomial energy-dependent potential
• Marchenko Equations and Norming Constants of the Matrix Zakharov-Shabat System
• Spectral Theory of the Klein–Gordon Equation in Krein Spaces
• Inverse scattering for Schrödinger operators with Miura potentials: I. Unique Riccati representatives and ZS-AKNS systems
• Scattering and inverse scattering for first order systems
• Inverse scattering and evolution equations
• Scattering and inverse scattering for first-order systems: II
• The Inverse Problem in the Quantum Theory of Scattering
• Non-self-adjoint Zakharov–Shabat operator with a potential of the finite asymptotic values. I. Direct spectral and scattering problems
• Scattering and inverse scattering for the 1-D Schrödinger equation with energy-dependent potentials
• Inverse scattering for the Dirac operator on the real line
• Inverse scattering on the line
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Rational reflection coefficients in inverse scattering for a Dirac system
• Dirac type and canonical systems: spectral and Weyl–Titchmarsh matrix functions, direct and inverse problems
• Weyl–Titchmarsh $M$-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators
• Solution of an inhomogeneous boundary-value problem with continuous-discrete parameters for discrete perturbations
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