Related papers: Scattering for the one dimensional Hartree Fock eq…
The reciprocity principle is that, when an emitted wave gets scattered on an object, the scattering transition amplitude does not change if we interchange the source and the detector - in other words, if incoming waves are interchanged with…
We consider the problem of fixed frequency acoustic scattering from a sound-soft flat screen. More precisely the obstacle is restricted to a two-dimensional plane and interacting with a arbitrary incident wave, it scatters acoustic waves to…
We solve the problem of electron scattering at a potential temporal step discontinuity. We show that the Schrodinger equation cannot account for scattering in this problem, necessitating resort to the Dirac equation, and that breaking gauge…
We derive the extension of the classical d'Alembert formula for the wave equation, which provides the analytical solution for the direct scattering problem for a medium with constant refractive index; this is achieved by employing results…
We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we…
A linear scattering problem for which incoming and outgoing waves are restricted to a finite number of radiation channels can be precisely described by a frequency-dependent scattering matrix. The entries of the scattering matrix, as…
In this paper, we consider the direct and inverse problem of scattering of time-harmonic waves by an unbounded rough interface with a buried impenetrable obstacle. We first study the well-posedness of the direct problem with a local source…
The generalized Benjamin-Bona-Mahony equation (gBBM) is a model for nonlinear dispersive waves which, in the long-wave limit, is approximately equivalent to the generalized Korteweg-de Vries equation (gKdV). While the long-time behaviour of…
In the context of elastic wave propagation in damaged solids, an analytical approach for scattering of antiplane waves by two-dimensional periodic arrays of cracks is developed. Before considering the study of arrays of cracks, the…
We present a theoretical study of linear wave scattering in one-dimensional nonlinear lattices by intrinsic spatially localized dynamic excitations or discrete breathers. These states appear in various nonlinear systems and present a…
A theoretical model based on two-point scatterers is suggested to investigate scattering of partially coherent radiation by a non-Hermitian localized structure, invariant under the simultaneous symmetry operations of parity inversion and…
We consider the question of scattering for the boson star equation in three space dimensions. This is a semi-relativistic Klein-Gordon equation with a cubic nonlinearity of Hartree type. We combine weighted estimates, obtained by exploiting…
In this paper, we consider the problem of the scattering of in-plane waves at an interface between a homogeneous medium and a metamaterial. The relevant eigenmodes in the two regions are calculated by solving a recently described non…
Direct phase-resolved simulations are performed to investigate the propagation and scattering of nonlinear ocean waves in fragmented sea ice. The numerical model solves the full time-dependent equations for nonlinear potential flow coupled…
This paper is concerned with acoustic scattering from a sound-soft trapezoidal surface in two dimensions. The trapezoidal surface is supposed to consist of two horizontal half-lines pointing oppositely, and a single finite vertical line…
The density matrix expansion is used to derive a local energy density functional for finite range interactions with a realistic meson exchange structure. Exchange contributions are treated in a local momentum approximation. A generalized…
In this paper, we study the scattering for the nonlinear beam equation $u_{tt}+\Delta^2u+mu+\mu |u|^{p-1}u=0$. Our results include two aspects. In the defocusing case we show that the scattering holds for $d=1$, which extends the result in…
The scattering of wave packets from a single slit and a double slit with the Schr\"odinger equation, is studied numerically and theoretically. The phenomenon of diffraction of wave packets in space and time in the backward region,…