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Approximation of the inverse scattering Steklov eigenvalues and the inverse spectral problem
In this paper, we consider the numerical approximation of the Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying...
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Multifrequency inverse obstacle scattering with unknown impedance boundary conditions using recursive linearization
In this paper, we consider the reconstruction of the shape and the impedance function of an obstacle from measurements of the scattered field at a...
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Inverse Problems for Trees
This chapter is devoted to the solution of the inverse problem for Schrödinger operators on metric trees.
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Inverse Scattering Transform and Dynamics of Soliton Solutions for Nonlocal Focusing Modified Korteweg-de Vries Equation
The Riemann–Hilbert problem is developed to study the general N -soliton solution of the nonlocal modified Korteweg-de Vries equation in this work....
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Live load matrix recovery from scattering data in linear elasticity
We study the numerical approximation of the inverse scattering problem in the two-dimensional homogeneous isotropic linear elasticity with an unknown...
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Direct and Inverse Scattering for the Matrix Schrödinger Equation
Authored by two experts in the field who have been long-time collaborators, this monograph treats the scattering and inverse scattering problems for...
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A numerical study of single source localization algorithms for phaseless inverse scattering problems
Phaseless inverse scattering problems appear often in practical applications since phaseless data are relatively easier to measure than the phased...
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A Remark on the Inverse Scattering Problem for the Perturbed Hill Equation
AbstractThe perturbed Hill equation in which the perturbed potential has finite first moment is considered. An integral equation for the kernel of...
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Uniqueness of the Inverse Transmission Scattering with a Conductive Boundary Condition
This paper considers the inverse acoustic wave scattering by a bounded penetrable obstacle with a conductive boundary condition. We will show that...
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Modified transmission eigenvalues for inverse scattering in a fluid–solid interaction problem
Target signatures are discrete quantities computed from measured scattering data that could potentially be used to classify scatterers or give...
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A Reduced Order Model Approach to Inverse Scattering in Lossy Layered Media
We introduce a reduced order model (ROM) methodology for inverse electromagnetic wave scattering in layered lossy media, using data gathered by an...
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Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions
In this topical review paper we provide a survey of classical and more recent results on the IST for one-dimensional scalar, vector and square matrix...
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Inverse problem for a random Schrödinger equation with unknown source and potential
In this paper, we study an inverse scattering problem associated with the time-harmonic Schrödinger equation where both the potential and the source...
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The a Priori and a Posteriori Error Estimates of DG Method for the Steklov Eigenvalue Problem in Inverse Scattering
In this paper, we study the discontinuous Galerkin finite element method for the Steklov eigenvalue problem arising in inverse scattering. We present...
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Scattering problems for the wave equation in 1D: D’Alembert-type representations and a reconstruction method
We derive the extension of the classical d’Alembert formula for the wave equation, which provides the analytical solution for the direct scattering...
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Quadrature Domains for the Helmholtz Equation with Applications to Non-scattering Phenomena
In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called...
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A Robust and High Precision Algorithm for Elastic Scattering Problems from Cornered Domains
The Navier equation is the governing equation of elastic waves, and computing its solution accurately and rapidly has a wide range of applications in...
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Multi-scale PDE Inverse Problem in Bacterial Movement
By their nature, biological systems evolve to complex structures, posing challenges for mathematical modelling that involve partial differential...
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To the Solution of the Inverse Problem of Scattering Theory on the Entire Line
AbstractSufficient conditions are given that ensure the validity of the main Faddeev–Marchenko theorem on the reconstruction of the potential of the...
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Multifrequency Inverse Problem of Scalar Acoustics: Remarks on Nonuniqueness and Solution Algorithm
A three-dimensional multifrequency inverse problem of acoustic sounding of a stationary inhomogeneous medium is considered. This nonlinear inverse...