Propagation Property and Application to Inverse Scattering for Fractional Powers of Negative Laplacian

DOI10.4208/EAJAM.050319.110619zbMath1462.81090arXiv1612.01683OpenAlexW2999559258MaRDI QIDQ4986589

Atsuhide Ishida

Publication date: 27 April 2021

Published in: East Asian Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.01683

zbMATH Keywords

inverse problemscattering theoryfractional Laplacian

Mathematics Subject Classification ID

Inverse scattering problems in quantum theory (81U40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) (2)-body potential quantum scattering theory (81U05) Fractional partial differential equations (35R11)

Related Items (4)

Time Domain Linear Sampling Method for Inverse Scattering Problems with Cracks ⋮ Finite Difference Method for Inhomogeneous Fractional Dirichlet Problem ⋮ Inverse Scattering Method for Constructing Multisoliton Solutions of Higher-Order Nonlinear Schrödinger Equations ⋮ Threshold between short and long-range potentials for non-local Schrödinger operators

Cites Work

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• Propagation properties of quantum scattering states
• On multidimensional inverse scattering in time-dependent electric fields
• On multidimensional inverse scattering in an external electric field asymptotically zero in time
• Pseudodifferential and Singular Integral Operators
• On inverse scattering problem for the Schrödinger equation with repulsive potentials
• On multidimensional inverse scattering for Stark Hamiltonians
• Asymptotic completeness for functions of the Laplacian perturbed by potentials and obstacles
• The geometrical approach to multidimensional inverse scattering

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