Scattering by acoustic boundary scatterers with small wave sizes and their reconstruction

Faddeev Eigenfunctions for Multipoint Potentials

“…Thus, basic formulas and equations of monochromatic inverse scattering are illustrated by explicit examples related to multipoint potentials. We think that the results of the present work can be used, in particular, for testing different monochromatic inverse scattering algorithms based on properties of the Faddeev functions ψ and h (see [2] as a work in this direction).…”

Faddeev eigenfunctions for point potentials in two dimensions

“…† Landau Institute of Theoretical Physics, Kosygin street 2, 117940 Moscow, Russia; e-mail: pgg@landau.ac.ru. ‡ CNRS (UMR 7641), Centre de Mathématiques Appliquées,École Polytechnique, 91128, Palaiseau, France; e-mail: novikov@cmap.polytechnique.fr k ∈ R 2 , k 2 = E > 0, where a priori unknown function f (k, l), k, l ∈ R 2 , k 2 = l 2 = E, arising in (2), is the classical scattering amplitude for (1). In addition, we consider the Faddeev eigenfunctions ψ for (1) (see [7], [13], [9]), specified by…”

Multipoint scatterers with bound states at zero energy

“…Example 1 Let n = 4, z j ∈ R 3 , |z j −z j ′ | = s > 0 for all j = j ′ , 1 ≤ j, j ′ ≤ 4, α j = α = −(4πs) −1 , and v be given by (2). Then E = 0 is a triple eigenvalue for equation (1) (i.e.…”

“…We consider the model of point scatterers in three dimensions, which goes back to the classical works [4], [6], [9], [3] and presented in detail in the book [1]. For more recent results on such models, see [5], [2], [7] and references therein. More precisely, we consider the stationary Schrödiger equation…”