Related papers: Acoustic Scattering and the Extended Korteweg deVr…
We develop direct scattering theory for one-dimensional Schr\"odinger operators with steplike potentials, which are asymptotically close to different Bohr almost periodic infinite-gap potentials on different half-axes.
Inverse scattering problem for the operator representing sum of the operator of the third derivative on semi-axis and of the operator of multiplication by a real function is studied in this paper. Properties of Jost solutions of such an…
A one-dimensional generalized nonlinear Schroedinger equation is considered, and the corresponding inverse scattering problem is analyzed when the potential is compactly supported and depends on the wave function. The unique recovery of the…
We continue the study of the theory of scattering for some long range Hartree equations with potential |x|^-gamma, performed in a previous paper, denoted as I, in the range 1/2 < gamma < 1. Here we extend the results to the range 1/3 <…
\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct…
We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time \pi on…
We continue the study of scattering theory for the system consisting of a Schr"odinger equation and a wave equation with a Yukawa type coupling in space dimension 3. In a previous paper we proved the existence of modified wave operators for…
In the present article, we assume that the first approximation of the scattering operator is given and that it has the logarithmic divergence. This first approximation allows us to construct the so called deviation factor. Using the…
We consider scattering theory for a pair of operators $H_0$ and $H=H_0+V$ on $L^2(M,m)$, where $M$ is a Riemannian manifold, $H_0$ is a multiplication operator on $M$ and $V$ is a pseudodifferential operator of order $-\mu$, $\mu>1$. We…
A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as…
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into…
We show theoretically and experimentally that the propagation of an acoustic wave in an airflow duct going through a pair of diaphragms, with equivalent amount of mean-flow-induced effective gain and loss, displays all the features of a…
We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. We construct flows on the moduli space of algebraic Riemann surfaces that preserve the periods of the corresponding…
In this paper, we consider inverse time-harmonic acoustic and electromagnetic scattering from locally perturbed rough surfaces in three dimensions. The scattering interface is supposed to be the graph of a Lipschitz continuous function with…
We prove that the inverse scattering problem for the Schr\"odinger operator with the separable potential can be reduced to the solving of a certain singular integral equation. We establish the uniqueness of the potential corresponding to…
The scattering problem under the influence of the Aharonov-Bohm (AB) potential is reconsidered. By solving the Lippmann-Schwinger (LS) equation we obtain the wave function of the scattering state in this system. In spite of working with a…
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…
In this paper we investigate the spectral and the scattering theory of Schr\"odinger operators acting on perturbed periodic discrete graphs. The perturbations considered are of two types: either a multiplication operator by a short-range or…
The correspondence between the steady state theory of current transfer and scattering theory in a system of coupled tight-binding models of 1-dimensional wires is explored. For weak interwire coupling both calculations give nearly identical…