76 citations · 458 across the 35 of their papers we have counts for
12 papers · 1 filter
Phase recovery from phaseless scattering data for discrete Schrödinger operators
Roman Novikov, Basant Lal Sharma
We consider scattering for the discrete Schrödinger operator on the square lattice , , with compactly supported potential. We give formulas for finding the p…
Creation and annihilation of point-potentials using Moutard-type transform in spectral variable
P. G. Grinevich, R. G. Novikov
We continue to develop the method for creation and annihilation of contour singularities in the --spectral data for the two-dimensional Schrödinger equation at fixed…
Moutard transform for the conductivity equation
P. G. Grinevich, R. G. Novikov
We construct Darboux-Moutard type transforms for the two-dimensional conductivity equation. This result continues our recent studies of Darboux-Moutard type transforms for generali…
An example of non-uniqueness for Radon transforms with continuous positive rotation invariant weights
Fedor Goncharov, Roman Novikov
We consider weighted Radon transforms along hyperplanes in with strictly positive weights . We construct an example of such a transform with non-trivial kernel $\mat…
A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy
Evgeny L. Lakshtanov, Roman G. Novikov, Boris R. Vainberg
We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or generic versions of the key…
Phaseless inverse scattering in the one-dimensional case
Roman Novikov
We consider the one-dimensional Schrödinger equation with a potential satisfying the standard assumptions of the inverse scattering theory and supported on the half-line .…
Formulas for phase recovering from phaseless scattering data at fixed frequency
Roman Novikov
We consider quantum and acoustic wave propagation at fixed frequency for compactly supported scatterers in dimension . In these framework we give explicit formulas for phas…
Explicit formulas and global uniqueness for phaseless inverse scattering in multidimensions
Roman Novikov
We consider phaseless inverse scattering for the Schrödinger equation with compactly supported potential in dimension . We give explicit formulas for solving this problem f…
Faddeev eigenfunctions for point potentials in two dimensions
Piotr Grinevich, Roman Novikov
We present explicit formulas for the Faddeev eigenfunctions and related generalized scattering data for point (delta-type) potentials in two dimensions. In particular, we obtain th…
On iterative reconstruction in the nonlinearized polarization tomography
Roman Novikov
We give uniqueness theorem and reconstruction algorithm for the nonlinearized problem of finding the dielectric anisotropy f of the medium from non-overdetermined polarization tomo…
On problem of polarization tomography, I
Roman Novikov, Vladimir Sharafutdinov
The polarization tomography problem consists of recovering a matrix function f from the fundamental matrix of the equation known for every geodesic of a giv…
The d-bar approach to approximate inverse scattering at fixed energy in three dimensions
Roman Novikov
We develop the d-bar approach to inverse scattering at fixed energy in dimensions of [Beals, Coifman 1985] and [Henkin, Novikov 1987]. As a result we propose a stable meth…