Singularities of the scattering kernel for two balls
The authors deal with the scattering by obstacles \({\mathcal O}\) formulated by Lax and Phillips, and consider an inverse problem similar to Majda's. It has been known that the back-scattering S(s,-\(\omega\),\(\omega)\) has at least two singular points for some \(\omega\) if \({\mathcal O}\) is not convex. In this paper, when \({\mathcal O}\) consists of two balls \({\mathcal O}_ 1\) and \({\mathcal O}_ 2\) in \({\mathbb{R}}^ 2\) or \({\mathbb{R}}^ 3\), they examine the whole distribution of the singular points of S(s,-\(\omega\),\(\omega)\) for some \(\omega\), and clarify the relation between this distribution and the distance of \({\mathcal O}_ 1\) and \({\mathcal O}_ 2\).
scientific article; zbMATH DE number 4040439