SCATTERING AND INVERSE SCATTERING FOR A 2ND-ORDER DIFFERENTIAL-EQUATION

The scattering and three inverse scattering problems for (d/dx) [a(x)(dpsi/dx)] +k2h(x)psi=Q(x)psi on the real axis are considered herein. In the first inverse scattering problem, Q(x) is recovered when a(x), h(x), and the scattering data are given. In the second inverse problem h(x) is recovered when a(x), Q(x), and the scattering data are known. In the third inverse problem, in case Q(x)=0, a(x) is recovered when h(x) and the scattering data are known. The inversion is illustrated with examples.