Iterative regularization schemes are considered based on derivatives with respect to variations of the boundary to reconstruct periodic scattering object from known data of a scattered field. Representations of the required derivatives are presented which help in understanding the ill-posed...

We describe a new realization for the no-response test by Luke and Potthast [SIAM J. Appl. Math.] to locate the unknown support of scatterers from the knowledge of the far field pattern of one scattered acoustic wave. The method uses a sampling set of surfaces and a special indicator function to...

In this numerical method for simultaneous reconstruction of permittivity and conductivity in the one-dimensional inverse problem for the Helmholtz equation, a system of Riccati equations with trace formulae is derived, then used to propagate reflection and transmission data into the interior of...

The inverse scattering method for solving the sine-Gordon equation in laboratory coordinates requires the analysis of the Faddeev–Takhtajan eigenvalue problem. This problem is not self-adjoint and the eigenvalues may lie anywhere in the complex plane, so it is of interest to determine...