Inverse scattering for the higher order Schrödinger operator with a first order perturbation

DOI10.1515/jiip-2018-0036zbMath1418.35132OpenAlexW2921168930MaRDI QIDQ2316693

Quan Zheng, Hua Huang, Zhiwen Duan

Publication date: 6 August 2019

Published in: Journal of Inverse and Ill-Posed Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip-2018-0036

zbMATH Keywords

inverse scatteringcomplex geometrical optics solutionshigher order Schrödinger operator

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Schrödinger operator, Schrödinger equation (35J10) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items

Inverse scattering problem for the high order Schrödinger operator at fixed angles scattering amplitude

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability of the inverse boundary value problem for the biharmonic operator: logarithmic estimates
• A global uniqueness theorem for an inverse boundary value problem
• Multidimensional inverse spectral problem for the equation \(-\Delta \psi -(v(x)-Eu(x))\psi =0\)
• Determining a first order perturbation of the biharmonic operator by partial boundary measurements
• Completeness of products of solutions and some inverse problems for PDE
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Inverse scattering for the magnetic Schrödinger operator
• Reconstructions from boundary measurements
• A special Green's function for the biharmonic operator and its application to an inverse boundary value problem
• The inverse scattering problem at fixed energy for the three-dimensional Schrödinger equation with an exponentially decreasing potential
• Global uniqueness for an inverse boundary problem arising in elasticity
• Inverse scattering problem for the Schrödinger equation with magnetic potential at a fixed energy
• Long range scattering for higher order Schrödinger operators
• Determining a magnetic Schrödinger operator from partial Cauchy data
• Fixed energy inverse problem for exponentially decreasing potentials
• Inverse boundary value problems for the perturbed polyharmonic operator
• Semiclassical Pseudodifferential Calculus and the Reconstruction of a Magnetic Field