Related papers: Inverse scattering on the half-line revisited
We present a novel method to estimate the stability of the Marchenko equation for finite data-sets. We show that we can derive a recursion relationship for the Fourier expansion coefficients of the kernel which is solved by the Marchenko…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
The direct and inverse scattering problems are analyzed for a first-order discrete system associated with the semi-discrete version of the derivative NLS system. The Jost solutions, the scattering coefficients, the bound-state dependency…
The inverse scattering problem, whose goal is to reconstruct an unknown scattering object from its scattered wave, is essential in fundamental wave physics and its wide applications in imaging sciences. However, it remains challenging to…
This paper corrects several errors in the author's previous papers (Journal of Spectral Theory 2016, Analysis and PDE 2014) on the Davey-Stewartson II (DS II) and modified Novikov-Veselov (mNV) equations. In each of these papers a proof was…
In this paper, we study the inverse medium scattering problem to reconstruct unknown inhomogeneous medium from far field patterns of scattered waves. In the first part of our work, the linear inverse scattering problem was discussed, while…
Direct and inverse scattering problems for a third-order self-adjoint differential operator on the whole axis are studied. This operator is the sum of three summands: operator of third derivative, operator of multiplication by a function,…
Solving inverse scattering problem for a discrete Sturm-Liouville operator with the fast decreasing potential one gets reflection coefficients $s_\pm$ and invertible operators $I+H_{s_\pm}$, where $ H_{s_\pm}$ is the Hankel operator related…
This article is devoted to inverse problems for nonlinear equations of the modified transfer, which can be regarded as a manageable problem. Various productions such problems for normal (unmodified) of the transport equation studied earlier…
We propose a method for reconstruction of the optical potential from scattering data. The algorithm is a two-step procedure. In the first step the real part of the potential is determined analytically via solution of the Marchenko equation.…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
This paper develops an efficient numerical method for the inverse scattering problem of a time-harmonic plane wave incident on a perfectly reflecting random periodic structure. The method is based on a novel combination of the Monte Carlo…
Inverse scattering theory is extended to one-dimensional Schr\"odinger problems with near-boundary singularities of the form $v(z\to 0)\simeq -z^{-2}/4+v_{-1}z^{-1}$. Trace formulae relating the boundary value $v_0$ of the nonsingular part…
An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…
We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is a similar to the inverse back-scattering…
In what follows we first set the context for inverse scattering in nuclear physics with a brief account of inverse problems in general. We then turn to inverse scattering which involves the S-matrix, which connects the interaction potential…
In this paper, we develop an inverse scattering transform for the integrable focusing nonlinear Schr\"odinger (NLS) equation on the half-line subject to a class of boundary conditions. The method is based on the notions of integrable…
We investigate inverse scattering problems for Dirac equations that arise as continuum models of waveguide arrays. We first establish the well-posedness of the forward models. For the associated inverse problems, we develop the inverse Born…
The Newton-Sabatier method for solving inverse scattering problem with fixed-energy phase shifts for a sperically symmetric potential is discussed. It is shown that this method is fundamentally wrong: in general it cannot be carried…
The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…