An overview of the author’s results is given. Property C stands for completeness of the set of products of solutions to homogeneous linear Sturm-Liouville equations. The inverse problems discussed include the classical ones (inverse scattering on a half-line, on the full line, inverse spectral problem), inverse scattering problems with incomplete data, for example, inverse scattering on the ful...

The Bethe ansatz equations of the 1-D SU(3) Hubbard model are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model. We first derive the scattering matrix of the SU(3) Hubbard model through the coordinate Bethe ansatz method. Then, with the help quantum inverse scattering method we solve the nested transfer matrix and give the eigenvalues, the eigenvectors a...

The Bethe ansatz equations of the 1-D SU(3) Hubbard model are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model. We first derive the scattering matrix of the SU(3) Hubbard model through the coordinate Bethe ansatz method. Then, with the help quantum inverse scattering method we solve the nested transfer matrix and give the eigenvalues, the eigenvectors a...

Our recent inverse scattering work has been to derive inverse scattering theory and algorithms that can be used to process practical experimental data. The theory makes use of computation of the forward scattering solution. Therefore, an eecient forward solver is instrumental to the rapid solution of the inverse scattering problem. The advantage of the more sophisticated theory over a linear th...

An important radiative process, used in several astrophysical contexts to generate high energy photons, is the inverse compton scattering. In this process, relativistic electrons transfer part of their kinetic energy to low energy photons thereby creating high energy photons. Conventional text book derivation (Rybicki & Lightman 1979) of this process uses the photon picture, kinematics of elect...

A review of the author’s results is given. Inversion formulas and stability results for the solutions to 3D inverse scattering problems with fixed energy data are obtained. Inversion of exact and noisy data is considered. The inverse potential scattering problem with fixed-energy scattering data is discussed in detail, inversion formulas for the exact and for noisy data are derived, error estim...

A generalization of the quantum inverse scattering method is proposed replacing the quantum group RLL commutation relations of Lax operators by reflection equation type RLRL commutation relations. Under some natural assumptions the most general algebra of this type allowing to construct the neccessary integrals of ⋆ Supported by the Science and Technology Fellowship Programme for Japan under th...

Hard photons well above 100GeV have to be generated in a future photon collider which essentially will be based on the infrastructure of the planned International Linear Collider (ILC). The energy of near-infrared laser photons will be boosted by Compton backscattering against a high-energy relativistic electron beam. For high effectiveness, a very powerful laser system is required that exceeds...

Inverse scattering from discrete targets with the single-input–multiple-output (SIMO), multiple-input–single-output (MISO) or multiple-input–multipleoutput (MIMO) measurements is analyzed by compressed sensing theory with and without the Born approximation. High-frequency analysis of (probabilistic) recoverability by the L1-based minimization/regularization principles is presented. In the absen...

We consider the electromagnetic inverse scattering problem of determining the support of an orthotropic or anisotropic anomaly in a homogeneous background medium from a knowledge of the electric far eld pattern corresponding to the scattering of electromagnetic plane waves. Our aim is to derive a linear integral equation of the rst kind from which the support of the anomaly can be found by exam...