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 $A(\beta ,{\alpha }_0,k)$ $\forall \beta \in S^2$, $\forall k>0,$ determine $q$ uniquely. Here ${\alpha }_0\in S^2$ is a fixed direction of the incident plane wave.

References in corpus (3)

• Stability of solutions to inverse scattering problems with fixed-energy data
• Uniqueness theorem for inverse scattering problem with non-overdetermined data
• Uniqueness of the solution to inverse scattering problem with backscattering data

Cited by in corpus (5)

• The fixed angle scattering problem and wave equation inverse problems with two measurements
• Uniqueness for time-dependent inverse problems with single dynamical data
• Inverse scattering with the data at fixed energy and fixed incident direction
• Numerical results of solving 3D inverse scattering problem with non-over-determined data
• Inverse obstacle scattering with non-over-determined data