The forward scattering series is an important and useful tool in constructing perturbative solutions to wave equation and understanding their relationship to their non-perturbative counterparts. When it converges, the series describes the total wavefield everywhere in a given medium as propagations in a reference medium and interactions with point scatterers. The method can be viewed as constru...

We define scattering data for the Newton equation in a potential V ∈ C2(Rn,R), n ≥ 2, that decays at infinity like r−α for some α ∈ (0, 1]. We provide estimates on the scattering solutions and scattering data and we prove, in particular, that the scattering data at high energies uniquely determine the short range part of the potential up to the knowledge of the long range tail of the potential....

We survey some of the highlights of inverse scattering theory as it has developed over the past fifteen years, with emphasis on uniqueness theorems and reconstruction algorithms for time harmonic acoustic waves. Included in our presentation are numerical experiments using real data and numerical examples of the use of inverse scattering methods to detect buried objects.

We present a new method to solve an inverse scattering problem for time-harmonic electromagnetic waves. The method is based on an equivalence relation of the inverse problem to a system of two integral equations. This system can be solved numerically by a recently developed spectral method for the direct scattering problem.

Mathematical modeling and algorithms of direct,and inverse electromagnetic scattering formulation due to biological tissues are investigated. The algorithms are used for a model based illustration technique within the microwave range. A number of methods is given to solve the direct,and inverse electromagnetic scattering problem in which the nonlinear and ill-posed nature of the problem are ack...

Property C, that is, completeness of the set of products of some solutions to SturmLiouville equations is proved. Several uniqueness theorems for various inverse scattering problems are obtained in a very simple way with the help of property C. Two classical uniqueness results for inverse scattering problem on the half-axis and for the inverse spectral problem are proved in a very short new way...

We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations radiationless sources, nonradiating incident waves, interior transmission eigen...

We consider the inverse scattering problem of determining both the shape and some of the physical properties of the scattering object from a knowledge of the (measured) electric and magnetic fields due to the scattering of an incident time harmonic electromagnetic wave at fixed frequency. We shall discuss the linear sampling method for solving the inverse scattering problem which does not requi...

Inverse scattering problem is discussed for the Maxwell’s equations. A reduction of the Maxwell’s system to a new Fredholm second-kind integral equation with a scalar weakly singular kernel is given for electromagnetic (EM) wave scattering. This equation allows one to derive a formula for the scattering amplitude in which only a scalar function is present. If this function is small (an assumpti...