This paper contains a solution with complete proofs of the main problems of the inverse
scattering at fixed energy E for the Schrödinger two-dimensional operator with decreasing …

Abstract CONTENTS Chapter I. A survey of the results § 1.1. The method of Faddeev in the
inverse scattering problem for the Schrödinger equation § 1.2. The results of Newton …

RG Novikov, “Multidimensional inverse spectral problem for the equation $-\Delta\psi+(v(x)-Eu(x))\psi=0$”,
Funktsional. Anal. i Prilozhen., 22:4 (1988), 11–22; Funct. Anal. Appl., 22:4 (1988), 263–272 …

The soliton represents one ofthe most important ofnonlinear phenomena in modern physics.
It constitutes an essentially localizedentity with a set ofremarkable properties. Solitons are …

Rapid progress in quantum theory brings us new important results which are often not
immediately clear to all who need them. But fortunately, this is also followed by …

We develop the∂¯-approach to inverse scattering at fixed energy in dimensions d≥ 3 of
Beals and Coifman (1984) and Henkin and Novikov (1987). As a result, we propose a stable …

The relations between the Faddeev functions and the functions of classical scattering theory
are found in the complex domain at fixed energy. For the three-dimensional case (without …

The process of reconstruction of two-dimensional refractive-absorbing scatterers by the
modified Novikov algorithm is considered. A generalization of this algorithm to the …

For the two-dimensional Schrödinger equation-Δ+ v (x) ψ= E ψ, x ∈ R^ 2, E= E_ fixed> 0 (*)
at a fixed positive energy with a fast decaying at infinity potential v (x) dispersion relations on …

Two variants of a functional-analytical algorithm intended for solving inverse tomography
problems are discussed and numerically carried out. The acoustic fields that are transmitted …