Uniqueness of the solution to inverse scattering problem with scattering data at a fixed direction of the incident wave

Abstract

Let q(x) be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data A(β, α[subscript]0, k) ∀β ∈ S[superscript]2, ∀k > 0, determine q uniquely. Here, α[subscript]0 ∈ S[superscript]2 is a fixed direction of the incident plane wave.