THE ONE-DIMENSIONAL INVERSE SCATTERING PROBLEM FOR THE WAVE-EQUATION

A constructive method is given for solving the inverse scattering problem for the wave equation on the line and half-line. The slowness function is assumed to have a derivative everywhere except at a finite number of points, and both it and its derivative are assumed to be functions of bounded variation. In addition, the slowness n(x) is required to tend to 1 sufficiently rapidly as x --> infinity. In this case the slowness function can be reconstructed from the reflection coefficient.