Numerical results of solving 3D inverse scattering problem with non-over-determined data

Abstract

We consider the 3D inverse scattering problem with non-over-determined scattering data. The data are the scattering amplitude $A(β, α_0, k)$ for all $β\in S_β^2$, where $S_β^2$ is an open subset of the unit sphere $S^2$ in $\mathbb{R}^3$, $α_0 \in S^2$ is fixed, and for all $k \in (a,b), 0 \leq a < b$. The basic uniqueness theorem for this problem belongs to Ramm \cite{R603}. In this paper, a numerical method is given for solving this problem and the numerical results are presented.