Related papers: Inverse scattering problems for the Hartree equati…
We transform an inverse scattering problem to be an interior transmission problem. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of…
Solutions of equations of geodesic deviation in three- and four- dimensional spaces obtained by the inverse scattering transform are considered. It is shown that in the case of three-dimensional space solutions of geodesic deviation…
We discuss a time-harmonic inverse scattering problem for the Navier equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…
In this paper, we study the blow up and scattering result of the solution to the focusing nonlinear Hartree equation with potential $$i\partial_t u +\Delta u - Vu = - (|\cdot|^{-3} \ast |u|^2)u, \qquad (t, x) \in \mathbb{R} \times…
We consider nonlinear Schr\"odinger equation with a Hartree-type nonlocal nonlinearity. The case where a nonlinear interaction potential grows at the spatial infinity is studied. By virtue of an effective decomposition of the nonlinearity…
The inverse scattering problem of the reconstruction of the unknown potential with compact support in the 3-d Schr\"odinger equation is considered. Only the modulus of the scattering complex valued wave field is known, whereas the phase is…
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explicitly constructed in terms of the scattering data. The main…
We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schr\"odinger equation with unknown source and potential terms. The well-posedness of the direct scattering problem is first…
The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…
This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…
The inverse scattering problem of the three-dimensional Schroedinger equation is considered at fixed scattering energy with spherically symmetric potentials. The phase shifts determine the potential therefore a constructive scheme for…
We study the theory of scattering for a class of Hartree type equations with long range interactions in arbitrary space dimension n > or = 1, including the case of Hartree equations with time dependent potential V(t,x) = kappa t^(mu -…
We show that in one dimension the transfer matrix M of any scattering potential v coincides with the S-matrix of an associated time-dependent non-Hermitian 2 x 2 matrix Hamiltonian H(\tau). If v is real-valued, H(\tau) is pseudo-Hermitian…
The inverse scattering transform for the defocusing-defocusing coupled Hirota equations is strictly discussed with non-zero boundary conditions at infinity including non-parallel boundary conditions, specifically referring to the asymptotic…
This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…
In this paper, we study the scattering theory for the cubic inhomogeneous Schr\"odinger equations with inverse square potential $iu_t+\Delta u-\frac{a}{|x|^2}u=\lambda |x|^{-b}|u|^2u$ with $a>-\frac14$ and $0<b<1$ in dimension three. In the…
This work investigates the scattering coefficients for inverse medium scattering problems. It shows some fundamental properties of the coefficients such as symmetry and tensorial properties. The relationship between the scattering…
We develop the d-bar approach to inverse scattering at fixed energy in dimensions $d\ge 3$ of [Beals, Coifman 1985] and [Henkin, Novikov 1987]. As a result we propose a stable method for nonlinear approximate finding a potential $v$ from…
In the context of the Cauchy problem for the Korteweg-de Vries equation we extend the inverse scattering transform to initial data that behave at plus infinity like a sum of Wigner-von Neumann type potentials with small coupling constants.…